\u 


THE 


PRINCIPLES  OF  LOGIC 


THE 


PRINCIPLES    OF    LOGIC 


BY 


F.  H.  BRADLEY 

LL.D.    GLASGOW 
FELLOW    OF    MFRTON   rqj.l.TR.av..    OXFORD 


LONDON 
KEGAN  PAUL,  TRENCH,  &  CO.,  i,  PATERNOSTER  SQUARE 

1883 


^-^ 


LONDON : 
PRINTED    BY    WILLIAM    CLOWES    AND    SONS,     LIMITED, 
--  STAMFORD  STREET   AND   CHARING   CROSS. 


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PREFACE. 


The  following  work  makes  no  claim  to  supply  any  syste- 
matic treatment  of  Logic.  I  could  not  pretend  to  have 
acquired  the  necessary  knowledge  ;  and  in  addition  I  confess 
that  I  am  not  sure  where  Logic  begins  or  ends.  I  have 
adopted  the  title  Prmciples  of  Logic,  because  I  thought  that 
my  enquiries  were  mainly  logical,  and,  for  logic  at  least,  must 
be  fundamental. 

I  feel  that  probability  is  against  me.  Experience  has 
shown  that  most  books  on  Logic  add  little  to  their  subject. 
There  is  however  one  reflection  which  may  weigh  in  my 
favour.  Both  in  England  andv-in  Germany  that  subject  is 
in  motion.  Logic  is  not  where  it  was,  and  can  not  remain 
where  it  is.  And  when  one  works  with  the  stream  a  slight 
effort  may  bring  progress. 

I  have  in  general  not  referred  to  those  works  to  which  I 
have  been  indebted.  Amongst  recent  writers  I  owe  most  to 
Lotze,  and  after  him  to  Sigwart.  Wundt's  book  would  have 
been  more  useful '  had  it  come  to  me  earlier  ;  and  I  may  say 
the  same  of  Bergmann's.  I  am  under  obligations  to  both 
Steinthal  and  Lazarus.  And  amongst  English  writers  I  have 
learned  most  from  the  late  Professor  Jevons.  I  may  mention 
here  that  I  should  have  owed  certain  observations  to  Mr. 
Balfour's  able  work,  had  I  not  seen  it  first  when  my  book  was 
completed.  I  should  be  glad  to  state  my  debts  in  detail,  and 
in  this  way  to  express  the  gratitude  I  feel,  but  I  doubt  if  it  is 
now  possible.  I  could  not  everywhere  point  out  the  original 
owners  of  my  borrowed  material,  and  I  could  not  clearly 
state  how  much  is  not  borrowed.  I  lay  no  claim  to  originality, 
except  that,  using  the  result  of  others'  labour,  I  in  some 
respects  have  made  a  sensible  advance. 


3o7S^ 


VI  PREFACE. 

I  wished  at  first  to  avoid  polemics  altogether.  But,  though 
I  have  not  sought  out  occasions  of  difference,  it  is  plain  that 
too  much  of  my  book  is  polemical.  My  impression  is  that  it 
will  not  suffice  to  teach  what  seems  true.  If  the  truth  is  not 
needed  the  reader  will  not  work  for  it,  nor  painfully  learn  it. 
And  he  hardly  will  need  it  where  he  stands  possessed  of  what 
seems  an  easy  solution.  Philosophy  now,  as  always,  is  con- 
fronted with  a  mass  of  inherited  prejudice.  And,  if  my 
polemics  bring  uneasiness  to  one  self-satisfied  reader,  I  may 
have  done  some  service. 

I  fear  that,  to  avoid  worse  misunderstandings,  I  must  say 
something  as  to  what  is  called  "  Hegelianism."  For  Hegel 
himself,  assuredly  I  think  him  a  great  philosopher  ;  but  I  never 
could  have  called  myself  an  Hegelian,  partly  because  I  can 
not  say  that  I  have  mastered  his  system,  and  partly  because 
I  could  not  accept  what  seems  his  main  principle,  or  at  least 
part  of  that  principle.  I  have  no  wish  to  conceal  how  much  I 
owe  to  his  writings  ;  but  I  will  leave  it  to  those  who  can 
judge  better  than  myself,  to  fix  the  limits  within  which  I  have 
followed  him.  As  for  the  "  Hegelian  School  "  which  exists  in 
our  reviews,  I  know  no  one  who  has  met  with  it  anywhere 
else. 

What  interests  me  is  something  very  different.  We  want 
no  system-making  or  systems  home-grown  or  imported. 
This  life-breath  of  persons  who  write  about  philosophy  is  not 
the  atmosphere  where  philosophy  lives.  What  we  want  at 
present  is  to  clear  the  ground,  so  that  English  Philosophy,  if 
it  rises,  may  not  be  choked  by  prejudice.  The  ground  can 
not  be  cleared  without  a  critical,  or,  if  you  prefer  it,  a 
sceptical  study  of  first  principles.  And  this  study  must  come 
short,  if  we  neglect  those  views  which,  being  foreign,  seem 
most  unlike  our  own,  and  which  are  the  views  of  men  who, 
differing  from  one  another,  are  alike  in  having  given  an 
attention  to  the  subject  which  we  have  not  given.  This,  I 
think,  is  a  rational  object  and  principle,  and  I  am  persuaded 
that  a  movement  which  keeps  to  this  line  will  not  be  turned 
back. 

In  conclusion  I  maybe  allowed  to  anticipate  two  criticisms 
which  will  be  passed  on  my  work.     One  reader  will  lament 


PREFACE.  Vll 

that  he  is  overdone  with  metaphysics,  while  another  will 
stand  on  his  right  to  have  far  more.  I  would  assure  the  first 
that  I  have  stopped  where  I  could,  and  as  soon  as  I  was  able. 
And  in  answer  to  the  second  I  can  only  plead  that  my 
metaphysics  are  really  very  limited.  This  does  not  mean 
that,  like  more  gifted  writers,  I  verify  in  my  own  shortcomings 
the  necessary  defects  of  the  human  reason.  It  means  that  on 
all  questions,  if  you  push  me  far  enough,  at  present  I  end  in 
doubts  and  perplexities.  And  on  this  account  at  least  no 
lover  of  metaphysics  will  judge  of  me  hardly.  Still  in  the  end 
perhaps  both  objectors  are  right.  If  I  saw  further  I  should 
be  simpler.  But  I  doubt  if  either  would  then  be  less  dis- 
satisfied. 


CONTENTS. 


In  this  Table  the  numbers  refer  to  the  sections  of  each  chapter. 


BOOK  I. 
JUDGMENT. 


CHAPTER  I.  . 

THE  GENERAL  NATURE  OF  JUDGMENT. 

What  judgment  is.  It  implies  ideas,  and  these  are  signs  (1-3).  A  sign, 
what  (4-6).  Two  senses  of  "idea"  (6-8).  In  Judgment  ideas  are 
meanings  (9).     Judgment  defined  (10),  and  errors  refuted  (11-12). 

Mistaken  views  criticized.  Judgment  not  "association"  (13-14);  nor 
practical  influence  (15) ;  nor  a  mere  junction,  nor  an  equation  of 
ideas  (16).     Truths  contained  in  the  above  errors  (17). 

Developjifment  of  Judgment.  It  is  a  late  product  (18),  because  at  first  the 
mind  has  no  ideas  proper  (19-20).  Conditions  required  for  origin  of 
Judgment  (21-22).  If  the  Association-theory  were  true  it  could 
never  have  appeared  (23)  ;  but  from  the  first  universals  operate  in 
the  mind  (24-26)  . .  ..  ..  ..  ..  ..  Pages  1-39 

CHAPTER  II. 

THE  CATEGORICAL  AND  HYPOTHETICAL  FORMS  OF  JUDGMENT. 

Judgment  is  about  fact  (i).  Preliminary  objections  answered  (2).  But 
how  if  all  judgment  is  hypothetical  (3)  ?  And  if  judgment  keeps  to 
ideas  it  all  is  hypothetical  (4-6).  This  true  of  universal  and  again  of 
both  classes  of  singular  judgments  (7-8). 

But  judgment  is  not  confined  to  ideas.     It  refers  to  present  reahty  (9). 
On  the  other  hand  it  does  not  refer  to  reality  as  present  (10).     This 
•    explained  and  defended  (11-14). 

Search  for  Categorical  Judgment.  I.  Analytic  Judgments  of  sense,  and 
their  varieties  (15-16).  Superstition  as  to  names  of  Individuals  (i7-i8)._ 
II.  Synthetic  judgments  of  sense.  How  can  these  refer  to  present 
reality  (19)  ?  But  they  can  not  refer  to  mere  ideas  (20-21).  Their 
true  subject  is  unique.  Thisness  and  This.  Idea  of  "  this  "  how  used 
^21-27). 


X  CONTENTS. 

But  how  then  can  Synthetic  Judgments  be  true  of  this  given  reahty  (28)  ? 
Because  the  reality  is  not  the  mere  appearance  (29-30).      These  judg- 
ments rest  on  continuity  of  content  (31),  and  that  upon  ideal  identity 
(32-33).     Past  and  future  are  not  phenomena  (34). 
Recapitulation    (35).      Memory  and  prediction  not  mere    imagination 
___(36=3-7).     Ideaof  Individual,  what  (38-39).    Non-phenomenal  Singular 


Judgments  (41).  Existential  Judgments  (42).  Transition  to  Abstract 
Universal  Judgments  (43). 
These  are  hypothetical  (44).  Collective  Judgments  really  singular  (45). 
Hypotheticals  can  not  be  reduced  to  Categoricals  (46-47).  A  suppo- 
sition, what  (48).  Real  assertion  contained  in  Hypothetical  Judg- 
ments (49-52).     They  are  all  universal  (53-55).     Result  (56). 

Pages  40-90 

CHAPTER  II.     {Continued) 

With  hypotheticals  we  seem  to  have  left  the  real  world,  but  have  reached 
the  world  of  Science  (57).  Presumption  against  the  singular  judgment 
of  sense  (58).  Its  claim  (59-60)  is  untenable  because  it  mutilates  the 
facts  (61-67).  It  is  conditioned  (68-70),  and  conditional  (71) ;  and  is 
even  false  (72-73).  It  is  an  impure  and  imperfect  hypothetical 
(74-78).     Result  (79-80).     Remaining  class  of  Judgments  (81). 

Pages  91-108 

CHAPTER  III.  \ 

THE  NEGATIVE  JUDGMENT.   Vv^'-^A' 

Negation  depends  on  the  real  (i),  but  is  more  ideal  than  affirmation 
is  (2-3).  It  is  not  the  denial  of  an  affirmation  (4),  nor  is  it  a  kind  of 
affirmation  (5),  nor  an  affection  of  the  copula  (6).  It  has  a  positive 
ground  which  is  not  explicit  (6-7). 

Opposition  and  Privation.  These  distinctions  here  not  vital  (8),  but  call 
for  explanation  (9-1 1).  Varieties  of  negative  judgment.  Negative 
Existentials  (12). 

Logical  negation  is  subjective,  and  is  no  real  determination  (13-14).  It 
does  not  assert  the  existence  of  the  contradictory  (15).  Idea  of  the 
contradictory,  what  (16).  The  asserted  contrary  not  explicit  (17). 
Contrary  opposition  not  dual  (18).  Ambiguity  of  denial.  It  rests  on 
covert  assertion  (19-20).         ..  ..  ..  ..  Pages  109-120 


CHAPTER  IV.  t\ 

THE   DISJUNCTIVE  JUDGMENT. 

It  is  not  a  mere  combination  of  hypotheticals  (1-2).  Its  basis  is  always 
categorical  (3-6).  Alternatives  are  rigidly  exclusive.  Erroneous 
views  on  this  point  (7-12).  What  disjunction  presupposes  (13). 
Recapitulation  (14) ...  ..  Pages  1 21-130 


CONTENTS.  XI 


CHAPTER  V. 

PRINCIPLES   OF   IDENTITY,   CONTRADICTION,   EXCLUDED   MIDDLE,   AND 
DOUBLE   NEGATION. 

Principle  of  Identity  must  not  be  a  tautology  (1-3).  What  (if  anything) 
it  should  mean  (4-9).  Principle  of  Contradiction  does  not  explain 
anything  (10).  What  it  means  (11-14).  Further  criticism  and  ex- 
planation (15-16).  Principle  of  Excluded  Middle  is  one  special  case 
of  disjunction  (16-19).  Goes  beyond  it,  how  (20-21).  Is  wrongly 
objected  to  (22).  Criticism  of  mistaken  views  (23-27).  Double 
Negation,  wrong  account  of  (21).  True  explanation  (29-31).  Erro- 
neous use  of  (A^£7/<?)      ..  ..  ..  ..  ..         Pages  13  i-i  54 


J 


CHAPTER  VI^ 

THE  QUANTITY  OF  JUDGMENTS. 

Extension  and  intension  (1-2).     Mistakes  about   "connotation"   (3-5). 

Law  of  inverse  proportion  of  intent  to  extent,  shown  to  be  erroneous 

(6-10). 
Every  judgment  has  two  aspects,  and  can  be  taken  both  extensionally  and 

in  intension  (11-12).      The   first  defended   against  erroneous  views 

(13-21).     The  second  explained,  and  mistakes  removed  (22-29). 
Universal,  particular,  and  singular  ;    what  these  mean,  and  how  far  they 

can  be'Peal  (30-36).     The  corresponding  judgments,  what  (37-43). 

Pages  155-180 

CHAPTER  VIlK 
THE  MODALITY  OF  JUDGMENTS. 

Modality  affects  not  the  form  but  the  content  of  Judgment  (1-3).  Logical 
modality,  what  (4-5).  The  Assertorical  (6).  The  Necessary  is 
hypothetical  (7-11).  And  so  is  the  Possible  (12).  Varieties  of  the 
latter  (13-15). 

Modality  does  not  exist  in  fact  (16).  This  shown  of  the  necessary  (17), 
and  the  possible  (18-19).  But  there  must  be  a  real  basis  for  necessity 
(20),  and  for  possibility  (21-22). 

Further  explanations.  The  Potential  not  real  (23).  Conditions,  as  such, 
not  facts  (24).  Permanent  Possibilities  ambiguous  (25).  The 
Problematic  and  Particular  Judgments  identical  (26).  The  Impos- 
sible, what  (27).  The  possible  not  the  same  as  the  mere  not-im- 
possible (28-31).  ^; 

Probability.  Its  principles  logical  (32).  Is  neither  objective  nor  subjec- 
tive (33).  Rests  on  an  exhaustive  disjunction  (34-36),  each  alternative 
of  which  is  equally  credible  X37""38)-  Expression  of  the  chances  by 
fractions  (39-41).  Inductive  probability  implies  no  fresh  principle 
(42-43). 


XU  CONTENTS. 

Errors  refuted.  Probability  objective  as  well  as  subjective  (44-45).  It 
does  not  in  its  essence  imply  a  series  (46-50)  ;  nor  a  knowledge  of  the 
future  (51).  Fiction  of  the  "  long  run"  (52-54),  and  the  truth  which 
underlies  this  (55-57).  Superstitious  beliefs  (58-59).  Transition  to 
Inference  (61-63)  ..  ..  ,.  ,.  ..  Pages  181-221 


BOOK  II.— PART  I. 
THE  GENERAL  NATURE  OF  INFERENCE. 


CHAPTER  I. 

SOME  CHARACTERISTICS  OF  REASONING. 

We  are  really  agreed  on  three  features  of  inference.  What  these  are 
(1-3).     Examples  (4)    ..         ..  ..  ..  ..         Pages  225-226 

CHAPTER  II. 

SOME   ERRONEOUS   VIEWS. 

The  major  premise  is  a  superstition  (i)*  And  the  syllogism  is  not  the  one 
type  of  reasoning  (2).  The  ordinary  syllogism  in  extension  criticized 
(3-5).  Principle  of  nota  notes  (6).  Possible  reform  of  the  syllogism 
(7-8).  Principle  of  *'  Related  to  same  are  related  to  each  other " 
criticized  (9-10)  ..  ..  ..  ..  ..         Pages  227-234 

CHAPTER  III. 

A  GENERAL  IDEA  OF  INFERENCE. 

Inference  a  perception  ensuing  on  a  synthesis  (i).  Demonstration  is 
seeing  in  a  logical  preparation,  and  that  is  an  ideal  construction  (2-4). 
Examples  (5).     Superstitions  to  be  abandoned  (6)   ,.     Pages  235-239 


CHAPTER  IV. 

PRINCIPLES   OF   REASONING. 

These  are  special  principles  of  interrelation  (1-2).  Examples  of  syntheses 
(3).  But  in  what  sense  are  they  principles  (4)  ?  Not  as  canons  and 
tests  of  individual  inferences  (5-6).  No  art  of  Reasoning  (7).  Illus- 
tration from  Casuistry  (8-9).     Inadequacy  of  the  syllogism  (10). 

Pages  240-249 


CONTENTS.  XUl 

CHAPTER  V. 

NEGATIVE   REASONING. 

Its  general  nature  (i)  and  special  principles  (2),  Can  you  argue  from 
two  negative  premises  ?  Yes,  but  not  from  two  bare  denials  (3-7). 
When  one  premise  is  negative  can  the  conclusion  be  affirmative  ?  On 
one  special  condition,  yes  (8-9)  ..  ..  ..  Pages  250-259 

CHAPTER  VI. 

TWO   CONDITIONS   OF   INFERENCE. 

Result  reached    (i).     An  identical  point  required  in   all  reasoning  (2). 

Mere  likeness  not  enough  (3).     Principle  of  Identity  of  Indiscemibles 

stated  and  defended  (4-9). 
And  one  premise  at  least  must  be  universal  (10-13)    ..         Pages  260-272 


BOOK  IL— PART  II. 

INFERENCE—CONTINUED. 


CHAPTER  I. 

THE   THEORY  OF  ASSOCIATION   OF   IDEAS. 

The  fact  of  psychical  association  is  certain,  but  the  theory  which  explains 
reproduction  by  the  "Laws  of  Association"  is  false  (1-7).  Main 
ground  of  objection  (8).     The  true  explanation  of  the  fact  (9-12). 

Errors  refuted.  No  association  by  Contiguity  (13-17),  even  if  assisted  by 
Similarity  (18).  Similarity  alone  is  left  (19),  and  this  too  is  a  fiction 
(20-22),  which  the  facts  do  not  require  (23-25).  The  true  explanation 
(26-27).  Misunderstandings  removed  (28-31).  Wolff  and  Maas 
adduced  (32).  An  objection  answered  (33).  Practical  conclusion 
(34-36). 

Note.     Indissoluble  Association  and  the  Chemistry  of  Ideas. 

Pages  273-321 

CHAPTER  II. 

THE  ARGUMENT  FROM  PARTICULARS  TO  PARTICULARS. 

This  discussion  has  been  anticipated  (1-2).  Supposed  evidence  for  the 
Argument  (3)  is  an  ignoratio  elenchi  (4-5).  We  never  argue  from  par- 
ticulars as  such  (6-9),  but  from  an  universal  (10- 11).  And  we  can  not 
do  otherwise  (12-13).  Mr.  Spencer's  theory  of  inference  to  be  passed 
over  (14)  ..  ..  ..  ..  ..  ..         Pages  322-328 


XIV  CONTENTS. 

CHAPTER  III. 
THE   INDUCTIVE   METHODS  OF  PROOF. 

The  question  limited  (1-2).  Complete  Induction  (3).  Mill's  Canons  of 
Induction.  Their  claim  to  be  demonstrative  (4-5).  But  (I)  they  can 
not  start  from  fact  (7-9).  And  (II)  their  conclusion  need  not  be 
more  general  than  some  of  their  premises  (10).  And  (III)  they  all 
have  a  logical  flaw  unless  you  confine  them  to  the  case  in  hand 
(11-14).     Result  (15-16)        Pages  329-342 

CHAPTER  IV. 
JEVONS'   EQUATIONAL  LOGIC. 

The  Enquiry  limited  and  subdivided  (1-2).  A.  Propositions  are  not 
equations,  and  can  not  assert  mere  identity  (3-7).  B.  Reasoning  does 
not  consist  in  Substitution  of  Similars.  It  rather  connects  differences 
(8-13).  C.  The  Indirect  Method  (14)  can  not  be  reduced  to  Substi- 
tution (15-18).  The  Logical  Machine.  Its  merits  and  defects  (19- 
22).     Result  (23)      ..  ..  ..  ..  ..         Pages  343-360 


BOOK  III.— PART  I. 

INFERENCE— CONTINUED. 


CHAPTER  I. 

THE   ENQUIRY   REOPENED. 

Our  former  account  of  inference  was  insufficient.  There  are  inferences 
which  will  not  come  under  our  formula  (1-9)        ..         Pages  361-364 

CHAPTER  II. 

FRESH  SPECIMENS  OF  INFERENCE. 

Tests  of  the  existence  of  inference  (1-3).  Claim  of  fresh  specimens.  A. 
Three-term  Constructions  (4-5).  B.  Arithmetic  and  Geometry 
(6-15).  C.  Comparison  and  Distinction  (16-17).  D.  Recognition 
(18).  E.  Dialectic  (19-22).  F.  Abstraction  (23-24).  G.  Disjunc- 
tive Inference  (25-29).     H.  Immediate  Inferences  (30-37)- 

Pages  365-395 


CONTENTS.  XV 

CHAPTER  III. 
GENERAL  CHARACTERISTICS  OF   INFERENCE. 

Further  character  of  inference  as  an  ideal  experiment  (1-4).  This  type 
verified  throughout  our  fresh  instances  (5-10). 

Not  every  mental  activity  is  reasoning  (11).  Judgment  is  not  inference 
(12-18)  ;  nor  is  all  Reproduction  (19-22)  ;  nor  is  Imagination  (23- 
24).     Result  obtained  (25)      ..  ..  ..  ..         Pages  396-411 

CHAPTER  IV. 

THE  MAIN  TYPES  OF  INFERENCE. 

Analysis  and  Synthesis  are  two  main  types  (i).  This  not  apparent  (2), 
but  shown  throughout  the  whole  of  our  instances  (3-7).  Tabular 
statement  (8) ••  ..         Pages  412-418 

CHAPTER  V. 

ANOTHER  FEATURE  OF  INFERENCE. 

A  central  identity  required  for  each  process  of  experiment  (i).  Difficulties 
(2-3).  The  identity  shown  in  Recognition  and  Dialectic  (4)  ;  and  in 
Comparison  and  Distinction  (5-6).  This  further  explained  (7-9). 
The  identity  shown  in  spatial  Construction  and  in  Arithmetic  (10-12)  ; 
and  in  Abstraction  (13)  ;  and  in  Disjunctive  Inference  (14).  Result 
(15)         Pages  419-429 

CHAPTER  VI. 
THE   FINAL  ESSENCE  OF  REASONING. 

Principles  of  our  processes  (i).  Analysis  and  Synthesis  are  two  sides  of 
one  process  (2).  Their  sameness  shown  (3),  and  their  differences 
pointed  out  (4-7).     Analytic  and  Synthetic  Methods  (8-10). 

Judgment  and  Inference,  how  related  (11).  Every  judgment  involves 
synthesis  and  analysis  (12-14)  ;  but  itself  is  not  inference  (15).  If 
however  we  go  back  far  enough,  judgment  and  inference  seem  two 
sides  of  one  process  (16-22).  Their  connection  shown  in  the  working 
of  Reproduction  (23-24). 

Beside  Analysis  and  Synthesis  there  is  a  third  principle  of  reasoning 
(25).  Defects  of  Analysis  and  Synthesis  (25-28).  These  defects 
suggest  a  self-developing  function  (29-30),  which  appears  in  our  third 
principle  (31-32).  Recapitulation  (33).  Self-developement  shows 
itself  through  the  whole  process  of  reasoning  (34-35).     Pages  430-454 


XVI  CONTENTS. 

CHAPTER  VII. 
THE   BEGINNINGS  OF  INFERENCE. 

Gulf  between  explicit  inference  and  the  beginnings  of  soul-life  (1-2). 
Yet  from  the  first  an  intellectual  activity  is  present,  which  slowly 
developes  (3-8).  Prevalent  errors  as  to  early  intelligence  (9-11). 
Obstacles  to  the  right  study  of  it  (12-15)   ••  ••         Pages  455-468 


BOOK  III.— PART  II. 
INFERENCE— CONTINUED. 


CHAPTER  I. 

FORMAL  AND   MATERIAL   REASONING. 

No  reasoning  with  a  bare  form  (2)  ;  nor  need  we  even  have  a  relative  form 
if  that  means  a  mere  formula  (3).  No  material  reasoning  if  that 
means  an  argument  from  the  particular  (4).  There  is  a  form  or 
principle  in  every  inference,  and  there  is  an  irrelevant  detail  (5-6). 
We  can  extract  this  form  (7)  ;  but  it  is  not  a  major  premise  (8-13). 
The  form  is  the  principle  which  neither  proves,  nor  is  proved  by,  the 
instances  (14-16)  ;  and  this  can  be  stated  in  a  syllogism  (17).  Other 
meanings  of  "formal"  (18)    ..  ..  ..  .,         Pages  469-483 


CHAPTER  II. 

THE  CAUSE  AND  THE   BECAUSE. 

Is  the  middle  the  cause  (i)?  Meaning  of  this  term  must  be  Hmited  (2). 
The  cause  is  known  by  reasoning,  since  it  imphes  ideal  reconstruction 
of  the  case  (3-5).  Futile  to  ask  if  cause  comes  from  mere  habit  (6). 
Explanation  not  perception  of  intermediate  detail  (7-10). 

But  the  reason  need  not  be  the  cause  (11).  Ambiguity  of  "  because  " 
(12).  The  psychical  cause  and  the  logical  ground  distinguished 
(13-14).  The  consequence  not  more  complex  than  the  cause  or 
ground  (15).     Result  (16) Pages  484-497 

CHAPTER  III. 

THE  VALIDITY  OF   INFERENCE. 

The  question  has  two  main  senses,  but  can  here  receive  no  final  answer 
(1-2).     Is  reasoning /<7rw^//)/ valid  ?     Not  if  we  have  interfered  to 


CONTENTS.  XVU 

make  the  conclusion  (3).  Do  we  interfere  in  Synthetical  Construction 
without  elision  (4-6),  or  with  ehsion  (7)?  Is  the  process  capricious 
in  Comparison,  etc.  (8-10),  and  again  in  Abstraction  (11-15)  ?  The 
Disjunctive  Argument  (16-20).  Sceptical  doubts  (21-22).  Result  (23). 
Is  a  conclusive  inference  practicable?  Question  explained  but  no 
answered  (24-25)         Pages  498-520 


CHAPTER  IV. 

THE  VALIDITY   OF   INFERENCE   (CONTINUED). 

Is  inference  valid  really  as  well  as  formally.?  Question  stated  (1-2). 
Inference  seems  not  always  true  of  things.  Instance  of  Comparison 
Three  alternatives  (3).  Does  reality  change  through  our  caprice,  or  in 
harmony,  or  does  it  merely  somehow  correspond  ?  Unless  we  utterly 
revolutionize  our  beliefs,  we  must  give  up  complete  identity  of  logic 
and  fact  (4-7). 

Reasoning  is  7ievero^\\.Q  true  of  presented  fact,  since  it  viwisth^  discursive 
(7-11).  Even  Dialectic,  because  discursive,  seems  unreal  (12).  Nor, 
if  logic  answered  to  the  known  series  of  phenomena,  would  it  even 
then  be  true  ;  for  that  series  is  not  given  but  inferred.  To  be  true  of 
the  presented  logic  must  be  true  to  sense,  which  is  impossible  (13-15). 

Can  we  then,  denying  the  truth  of  sense-presentation,  take  reality  itself  as 
logical  truth  ?  Another  alternative  opposes  us,  and  our  logic  still  may 
prove  untrue  (16).  Yet  why  should  truth  and  reality  have  exactly  the 
same  nature  (17)  ?     Anyhow  logic  can  not  copy  phenomena. 

Pages  521-534 


THE  PRINCIPLES  OF  LOGIC 

BOOK  I. 

JUDGMENT. 


CHAPTER  I. 
THE  GENERAL  NATURE  OF  JUDGMENT.  , 

§  I.  It  is  impossible,  before  we  have  studied  Logic,  to 
know  at  what  point  our  study  should  begin.  And,  after  we 
have  studied  it,  our  uncertainty  may  remain.  In  the  absence 
of  any  accepted  order  I  shall  offer  no  apology  for  beginning 
with  Judgment.  If  we  incur  the  reproach  of  starting  in  the 
middle,  we  may  at  least  hope  to  touch  the  centre  of  the 
subject. 

The  present  chapter  will  deal  with  the  question  of 
judgment  in  general.  It  will  (i)  give  some  account  of  the 
sense  in  which  the  term  is  to  be  used  :  it  will  (ll)  criticize, 
in  the  second  place,  a  considerable  number  of  erroneous 
views :  and  will  end  (ill)  with  some  remarks  on  the  develope- 
ment  of  the  function. 

I.  In  a  book  of  this  kind  our  arrangement  must  be 
arbitrary.  The  general  doctrine  we  are  at  once  to  lay  down, 
really  rests  on  the  evidence  of  the  following  chapters.  If 
it  holds  throughout  the  main  phenomena  of  the  subject, 
while  each  other  view  is  in  conflict  with  some  of  them,  it  seems 
likely  to  be  the  true  view.  But  it  can  not,  for  this  reason,  be 
put  forward  at  first,  except  provisionally. 

Judgment  presents  problems  of  a  serious  nature  to  both 

B 


2  ■  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

, f)sychology  and  metaphysics.     Its  relation  to  other  psychical 

•phenomena,  their  entangled  development  from  the  primary 
basis  of  soul-life,  and  the  implication  of  the  volitional  with  the 
intellectual  side  of  our  nature  on  the  one  hand,  and  on  the 
other  hand  the  difference  of  subject  and  object,  and  the 
question  as  to  the  existence  of  any  mental  activity,  may  be 
indicated  as  we  pass.  But  it  will  be  our  object,  so  far  as  is 
possible,  to  avoid  these  problems.  We  do  not  mainly  want 
to  ask.  How  does  judgment  stand  to  other  psychical  states, 
and  in  ultimate  reality  what  must  be  said  of  it.  Our  desire 
is  to  take  it,  so  far  as  we  can,  as  a  given  mental  function  ;  to 
discover  the  general  character  which  it  bears,  and  further  to 
fix  the  more  special  sense  in  which  we  are  to  use  it. 

§  2.  I  shall  pass  to  the  latter  task  at  once.  Judgment,  in 
the  strict  sense,  does  not  exist  where  there  exists  no  know- 
I  ledge  of  truth  and  falsehood  ;  and,  since  truth  and  falsehood 
depend  on  the  relation  of  our  ideas  to  reality,  you  can  not  have 
judgment  proper  without  ideas.  '  And  perhaps  thus  much  is 
obvious.  But  the  point  I  am  going  on  to,  is  not  so  obvious. 
,  Not  only  are  we  unable  to  judge  before  we  use  ideas,  but, 
strictly  speaking,  we  can  not  judge  till  we  use  them  as  ideas. 
We  must  have  become  aware  that  they  are  not  realities, 
that  they  are  mere  ideas,  signs  of  an  existence  other  than 
themselves.  Ideas  are  not  ideas  until  they  are  symbols,  and, 
before  we  use  symbols,  we  can  not  judge. 

§  3.  We  are  used  to  the  saying,  "This  is  nothing  real, 
it  is  a  mere  idea."  And  we  reply  that  an  idea,  within 
my  head,  and  as  a  state  of  my  mind,  is  as  stubborn  a  fact 
as  any  outward  object.  The  answer  is  well-nigh  as  familiar 
as  the  saying,  and  my  complaint  is  that  in  the  end  it  grows 
much  too  familiar.  In  England  at  all  events  we  have  lived 
too  long  in  the  psychological  attitude.  We  take  it  for 
granted  and  as  a  matter  of  course  that,  like  sensations  and 
emotions,  ideas  are  phenomena.  And,  considering  these 
phenomena  as  psychical  facts,  we  have  tried  (with  what 
success  I  will  not  ask)  to  distinguish  between  ideas  and 
sensations.  But,  intent  on  this,  we  have  as  good  as  for- 
gotten the  way  in  which  logic  uses  ideas.  We  have  not 
seen  that  in   judgment  no  fact    ever  is  just    that    which    it 


Chap.  I.]        THE   GENERAL   NATURE   OF  JUDGMENT.  3 

means,  or  can  mean  what  it  is ;  and  we  have  not  learnt  that, 
wherever  we  have  truth  or  falsehood,  it  is  the  signification  we 
use,  and  not  the  existence.  We  never  assert  the  fact  in  our 
heads,  but  something  else  which  that  fact  stands  for.  And  if 
an  idea  were  treated  as  a  psychical  reality,  if  it  were  taken  by 
itself  as  an  actual  phenomenon,  then  it  would  not  represent 
either  truth  or  falsehood.  When  we  use  it  in  judgment,  it 
must  be  referred  away  from  itself.  If  it  is  not  the  idea  of 
some  existence,  then,  despite  its  own  emphatic  actuality,  its 
content  remains  but  "  a  mere  idea."  It  is  a  something  which, 
in  relation  to  the  reality  we  mean,  is  nothing  at  all. 

§  4.  For  logical  purposes  ideas  are  symbols,  and  they  are 
nothing  but  symbols.  And,  at  the  risk  of  common-place,  before 
I  go  on,  I  must  try  to  say  what  a  symbol  is. 

In  all  that  is  we  can  distinguish  two  sides,  (i)  existence 
and  (ii)  content.  In  other  words  we  perceive  both  that  it  is 
and  what  it  is.  BjoMn^nything  that  is  a  symbol  we  have 
also  a  third  side,  its  signification,  or  that  which  it  means.  We 
need  not  dwell  on  the  two  first  aspects,  for  we  are  not  concerned 
with  the  metaphysical  problems  which  they  involve.  For  a 
fact  to  exist,  we  shall  agree,  it  must  be  something.  It  is  not 
real  unless  it  has  a  character  which  is  different  or  distinguish- 
able from  that  of  other  facts.  And  this,  which  makes  it  what 
it  is,  we  call  its  content.  We  may  take  as  an  instance  any 
coxnmon  perception.  The  complex  of  qualities  and  relations 
it  contains,  makes  up  its  content,  or  that  which  it  is ;  and, 
while  recognizing  this,  we  recognize  also,  and  in  addition,  that 
it  is.  Every  kind  of  fact  must  possess  these  two  sides  of 
existence  and  content,  and  we  propose  to  say  no  more  about 
them  here. 

But  there  is  a  class  of  facts  which  possess  an  other  and 
additional  third  side.  They^  have  a "  meaning ;  and  by  a 
sign  we  understand  any  sort  of  fact  which  is  used  with  a 
meaning.  The  meaning  may  be  part  of  the  original  content, 
or  it  may  have  been  discovered  and  even  added  by  a  further 
extension.  Still  this  makes  no  difference.  Take  anything 
which  can  stand  for  anything  els.e,  and  you  have  a  sign. 
Besides  its  own  private  existence  and  content,  it  has  this  third 
aspect.     Thus  every  flower  exists  and  has  its  own  qualities, 

B  2 


4  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

but  not  all  have  a  meaning.  Some  signify  nothing,  while 
others  stand  generally  for  the  kind  which  they  represent? 
while  others  again  go  on  to  remind  us  of  hope  or  love. 
But  the  flower  can  never  itself  be  what  it  means. 

A  symbol  is  a  fact  which  stands  for  something  else,  and 
by  this,  we  may  say,  it  both  loses  and  gains,  is  degraded  and 
exalted.  In  its  use  as  a  symbol  it  foregoes  individuality,  and 
self-existence.  It  is  not  the  main  point  that  this  rose  or 
forget-me-not,  and  none  other,  has  been  chosen.  We  give  it, 
or  we  take  it,  for  the  sake  of  its  meaning  ;  and  that  may 
prove  true  or  false  long  after  the  flower  has  perished.  The 
word  dies  as  it  is  spoken,  but  the  particular  sound  of  the 
mere  pulsation  was  nothing  to  our  minds.  Its  existence  was 
lost  in  the  speech  and  the  significance.  The  paper  and  the 
ink  are  facts  unique  and  with  definite  qualities.  They  are  the 
same  in  all  points  with  none  other  in  the  world.  But,  in 
reading,  we  apprehend  not  paper  or  ink,  but  what  they 
represent ;  and,  so  long  as  only  they  stand  for  this,  their 
private  existence  is  a  matter  of  indifference.  A  fact  taken 
as  a  symbol  ceases  so  far  to  be  fact.  It  no  longer  can  be 
said  to  exist  for  its  own  sake,  its  individuality  is  lost  in  its 
universal  meaning.  It  is  no  more  a  substantive,  but  be- 
comes the  adjective  that  holds  of  another.  But,  on  the 
other  hand,  the  change  is  not  all  loss.  By  merging  its  own 
quality  in  a  wider  meaning,  it  can  pass  beyond  itself  and 
stand  for  others.  It  gains  admission  and  influence  in  a  world 
which  it  otherwise  could  not  enter.  The  paper  and  ink  cut 
the  throats  of  men,  and  the  sound  of  a  breath  may  shake  the 
world. 

We  may  state  the  sum  briefly.  A  sign  is  any  fact  that 
has  a  meaning,  and  meaning  consists  of  a  part  of  the 
content  (original  or  acquired),  cut  off',  fixed  by  the  mind,  and 
considered  apart  from  the  existence  of  the  sign.^ 

*  It  would  not  be  correct  to  add,  "  and  referred  away  to  another  real 
subject ;  "  for  where  we  think  without  judging,  and  where  we  deny,  that 
description  would  not  be  applicable.  Nor  is  it  the  same  thing  to  have 
an  idea,  and  to  judge  it  possible.  To  think  of  a  chimasra  is  to  think  of 
it  as  real,  but  not  to  judge  it  even  possible.  And  it  is  not  until  we  have 
found  that  all  meaning  must  be  adjectival,  that  with  every  idea  we  have 
even  the  suggestion  of  a  real  subject  other  than  itself. 


Chap.  I.]         THE  GENERAL   NATURE   OF  JUDGMENT.  5 

§5.1  must  be  permitted  at  this  point  to  make  a  digression, 
which  the  reader  may  omit,  if  he  does  not  need  it.  Through- 
out this  volume  I  do  not  intend  to  use  the  word  "  symbol " 
as  distinct  from  "sign,"  though  there  is  a  difference  which 
elsewhere  might  become  of  importance.  A  symbol  is  certainly 
always  a  sign,  but  the  term  may  be  appropriated  to  signs  of  a 
very  special  character.  In  contrast  with  a  symbol  a  sign  may 
be  arbitrary.  It  can  not,  of  course,  be  devoid  of  meaning, 
for,  in  that  case,  it  would  be  unable  to  stand  for  anything. 
But  it  may  stand  for  that  with  which  internally  it  is  not 
connected,  and  with  which  it  has  been  joined  by  arbitrary 
chance.  But  even  when  signs  have  a  natural  meaning,  when 
their  content  carries  us  direct  to  the  object  of  which  they  are 
used,  yet,  if  we  take  symbol  in  a  narrow  sense,  a  natural 
sign  need  not  be  a  symbol.  We  may  restrict  the  term  to 
secondary  signs.  For  example  a  lion  is  the  symbol  of  courage, 
and  a  fox  of  cunning,  but  it  would  be  impossible  to  say  that 
the  idea  of  a  fox  stands  for  cunning  directly.  We  mean  by  it 
first  the  animal  called  a  fox,  and  we  then  use  this  meaning  to 
stand  as  the  sign  for  one  quality  of  the  fox.  Just  as  the 
image  or  presentation  of  a  fox  is  taken  by  us  in  one  part  of  its 
content,  and  referred  away  to  another  subject,  so  this  meaning 
itself  suffers  further  mutilation  :  one  part  of  its  content  is 
fixed  by  the  mind  and  referred  further  on  to  a  second  subject, 
viz.  the  quality  in  general,  wherever  found.  It  makes  no 
difference  whether  we  begin  with  an  image  or  a  sensible 
perception,  for  the  perception  itself,  before  it  can  be  used, 
must  be  taken  ideally,  recognized,  that  is,  in  one  part  of  its 
content.  And  the  distinction  again  between  the  symbolism 
that  is  unconscious,  and  that  which  is  reflective,  does  not  touch 
the  main  principle. 

In  order  to  obviate  possible  objections,  I  have  thought  it 
best  to  make  these  remarks  ;  but  since  I  propose  to  use  sign 
and  symbol  quite  indifferently,  the  discussion  has  hardly  any 
bearing  on  my  argument. 

§  6.  We  might  say  that,  in  the  end,  there  are  no  signs 
save  ideas,  but  what  I  here  wish  to  insist  on,  is  that,  for  logic 
at  least,  all  ideas  are  signs.  Each  we  know  exists  as  a 
psychical  fact,  and  with   particular   qualities   and    relations. 


6  THE  PRINCIPLES  OF  LOGIC.  [Book  1, 

It  has  its  speciality  as  an  event  in  my  mind.  It  is  a  hard 
individual,  so  unique  that  it  not  only  differs  from  all  others, 
but  even  from  itself  at  subsequent  moments.  And  this 
character  it  must  bear  when  confined  to  the  two  aspects  of 
existence  and  content.  But  just  so  long  as,  and  because,  it 
keeps  to  this  character,  it  is  for  logic  no  idea  at  all.  It 
becomes  one  first  when  it  begins  to  exist  for  the  sake  of  its 
meaning.  And  its  meaning,  we  may  repeat,  is  a  part  of  the 
content,  used  without  regard  to  the  rest,  or  the  existence.  I 
have  the  "  idea  "  of  a  horse,  and  that  is  a  fact  in  my  mind, 
existing  in  relation  with  the  congeries  of  sensations  and 
emotions  and  feelings,  which  make  my  momentary  state.  It 
has  again  particular  traits  of  its  own,  which  may  be  difftcult 
to  seize,  but  which,  we  are  bound  to  suppose,  are  present.  It 
is  doubtless  unique,  the  same  with  no  other,  nor  yet  with 
itself,  but  alone  in  the  world  of  its  fleeting  moment.  But,  for 
logic,  and  in  a  matter  of  truth  and  falsehood,  the  case  is  quite 
changed.  The  "  idea "  has  here  become  an  universal,  since 
everything  else  is  subordinate  to  the  meaning.  That  con- 
nection of  attributes  we  recognize  as  horse,  is  one  part  of  the 
content  of  the  unique  horse-image,  and  this  fragmentary  part 
of  the  psychical  event  is  all  that  in  logic  we  know  of  or  care 
for.  Using  this  we  treat  the  rest  as  husk  and  dross,  which 
matters  nothing  to  us,  and  makes  no  difference  to  the  rest. 
The  "  idea,"  if  that  is  the  f^l&b£sal  state,  is  in  logic  a  symbol. 
But  it  is  better  to  say,  the  idea  zs  the  meaning,  for  existence 
and  unessential  content  are  wholly  discarded.  The  idea,  in 
the  sense  of  mental  image,  is  a  sign  of  the  idea  in  the  sense  of 
meaning. 

§  7.  These  two  senses  of  idea,  as  the  symbol  and  the 
symbolized,  the  image  and  its  meaning,  are  of  course  known 
to  all  of  us.  But  the  reason  why  I  dwell  on  this  obvious 
distinction,  is  that  in  much  of  our  thinking  it  is  systematically 
disregarded.  "  How  can  any  one,"  we  are  asked,  "  be  so 
foolish  as  to  think  that  ideas  are  universal,  when  every  single 
idea  can  be  seen  to  be  particular,  or  talk  of  an  idea  which 
remains  the  same,  when  the  actual  idea  at  each  moment 
varies,  and  we  have  in  fact  not  one  identical  but  many 
similars } "     But  how  can  any  one,  we  feel  tempted  to  reply, 


Chap.  I.]        THE   GENERAL   NATURE   OF  JUDGMENT.  7 

suppose  that  these  obvious  objections  are  unknown  to  us? 
When  I  talk  of  an  idea  which  is  the  same  amid  change,  I  do 
not  speak  of  that  psychical  event  which  is  in  ceaseless  flux, 
but  of  one  portion  of  the  content  which  the  mind  has  fixed,  and 
which  is  not  in  any  sense  an  event  in  time.  I  am  talking  of 
the  meaning,  not  the  series  of  symbols,  the  gold,  so  to  speak, 
not  the  fleeting  series  of  transitory  notes.  The  belief  in 
universal  ideas  does  not  involve  the  conviction  that  abstrac- 
tions exist,  even  as  facts  in  my  head.  The  mental  event  is 
unique  and  particular,  but  the  meaning  in  its  use  is  cut  off 
from  the  existence,  and  from  the  rest  of  the  fluctuating 
content.  It  loses  its  relation  to  the  particular  symbol  :  it 
stands  as  an  adjective,  to  be  referred  to  some  subject,  but 
indifferent  in  itself  to  every  special  subject. 

The  ambiguity  of  "  idea  "  may  be  exhibited  thus.  Thesis, 
On  the  one  hand  no  possible  idea  can  be  that  which  it  means. 
Antithesis,  On  the  other  hand  no  idea  is  anything  but  just 
Avhat  it  means.  In  the  thesis  the  idea  is  the  psychical  im.age  : 
in  the  antithesis  the  idea  is  the  logical  signification.  In  the 
first  it  is  the  whole  sign,  but  in  the  second  it  is  nothing  but 
the  symbolized.  In  the  sequel  I  intend  to  use  idea  mainly  in 
the  sense  of  meaning* 

§  8.  For  logical  purposes  the  psychological  distinction  of 
idea  and  sensation  may  be  said  to  be  irrelevant,  while  the 
distinction  of  idea  and  fact  is  vital.  The  image,  or  psycho- 
logical idea,  is  for  logic  nothing  but  a  sensible  reality.  It 
is  on  a  level  with  the  mere  sensations  of  the  senses.     For 

*  There  are  psychological  difficulties  as  to  universal  ideas,  and  we 
feel  them  more,  the  more  abstract  the  ideas  become.  The  existence  and 
the  amount  of  the  particular  imagery  or  sensuous  environment,  give  rise  to 
questions.  But  these  questions  need  not  be  considered  here,  for  they 
have  no  logical  importance  whatever.  I  assume,  after  Berkeley,  that  the 
mental  fact  contains  always  an  irrelevant  sensuous  setting,  however  hard 
it  may  be  to  bring  this  always  to  consciousness.  But  I  must  repeat  that 
this  is  not  a  vital  question.  It  is  a  mistake  in  principle  to  try  to  defend 
the  reality  of  universals  by  an  attempt  to  show  them  as  psychical  events 
existing  in  one  moment.  For  if  the  universal  we  use  in  logic  had  actual 
existence  as  a  fact  in  my  mind,  at  all  events  I  could  not  use  it  as  that 
fact.  You  must  at  any  rate  abstract  from  the  existence  and  external 
relations,  and  how  much  further  the  abstraction  is  to  go  seems  hardly  an 
important  or  vital  issue. 


8  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

both  are  facts  and  neither  are  meanings.  Neither  are  cut 
from  a  mutilated  presentation,  and  fixed  as  a  connection. 
Neither  are  indifferent  to  their  place  in  the  stream  of 
psychical  events,  their  time  and  their  relations  to  the  pre- 
sented congeries.  Neither  are  adjectives  to  be  referred  from 
their  existence,  to  live  on  strange  soils,  under  other  skies,  and 
through  changing  seasons.  The  lives  of  both  are  so  entangled 
with  their  environment,  so  one  with  their  setting  of  sensuous 
particulars,  that  their  character  is  destroyed  if  but  one  thread 
is  broken.  Fleeting  and  self-destructive  as  is  their  very 
endurance,  wholly  delusive  their  supposed  individuality,  mis- 
leading and  deceptive  their  claim  to  reality,  yet  in  some 
sense  and  somehow  they  are.  They  have  existence  ;  they  are 
"not  thought  but  given.*  But  an  idea,  if  we  use  idea  of  the 
meaning,  is  neither  given  nor  presented  but  is  taken.  It 
can  not  as  such  exist.  It  can  not  ever  be  an  event,  with  a 
place  in  the  series  of  time  or  space.  It  can  be  a  fact  no  more 
inside  our  heads  than  it  can  outside  them.  And,  if  you  take 
this  mere  idea  by  itself,  it  is  an  adjective  divorced,  a  parasite 
cut  loose,  a  spirit  without  a  body  seeking  rest  in  another,  an 
abstraction  from  the  concrete,  a  mere  possibility  which  by 
itself  is  nothing. 

§  9.  These  paradoxical  shadows  and  ghosts  of  fact  are  the 
ideas  we  spoke  of,  when  we  said.  Without  ideas  no  judgment ; 
and,  before  we  proceed,  we  may  try  to  show  briefly  that  in 
predication  we  do  not  use  the  mental  fact,  but  only  the 
meaning.  The  full  evidence  for  this  truth  must  however  be 
sought  in  the  whole  of  what  follows. 

(i)  In  the  first  place  it  is  clear  that  the  idea,  which  we  use 
as  the  predicate  of  a  judgment,  is  not  my  mental  state  as 
such.  "  The  whale  is  a  mammal  "  does  not  qualify  real  whales 
by  my  mammal-image.  For  that  belongs  to  me,  and  is  an 
event  in  my  history  ;  and,  unless  I  am  Jonah,  it  can  not  enter 
into  an  actual  whale.  We  need  not  dwell  on  this  point,  for 
the  absurdity  is  patent.  If  I  am  asked.  Have  you  got  the 
idea  of  a  sea-serpent  ?  I  answer,  Yes.  And  again,  if  I  am 
asked,  But  do  you  believe  in  it,  Is  there  a  sea-serpent }  I 
understand  the  difference.  The  enquiry  is  not  made  about 
*  This  statement  is  subject  to  correction  by  Chapter  II. 


Chap.  I.]        THE   GENERAL   NATURE  OF  JUDGMENT.  9 

my  psychical  fact.  No  one  wishes  to  know  if  that  exists 
outside  of  my  head  ;  and  still  less  to  know  if  it  really  exists 
ijoside.  For  the  latter  is  assumed,  and  we  can  not  doubt  it. 
In  short  the  contention  that  in  judgment  the  idea  is  my  own 
state  as  such,  would  be  simply  preposterous. 

(ii)  But  is  it  possible,  secondly,  that  the  idea  should  be 
the  image,  not  indeed  as  my  private  psychical  event,  but  still 
as  regards  the  whole  content  of  that  image  ? '  We  have  a 
mental  fact,  the  idea  of  mammal.  Admit  first  that,  as  it 
exists  and  inhabits  my  world,  we  do  not  predicate  it.  Is 
there  another  possibility  ?  The  idea  perhaps  might  be  used 
apart  from  its  own  existence,  and  in  abstraction  from  its 
relations  to  my  psychical  phenomena,  and  yet  it  might  keep, 
without  any  deduction,  its  own  internal  content.  The 
"  mammal "  in  my  head  is,  we  know,  not  bare  mammal,  but 
is  clothed  with  particulars  and  qualified  by  characters  other 
than  mammality ;  and  these  may  vary  with  the  various 
appearances  of  the  image.*  And  we  may  ask.  Is  this  whole 
image  used  in  judgment }  Is  this  the  meaning  ?  But  the 
answer  must  be  negative. 

We  have  ideas  of  redness,  of  a  foul  smell,  of  a  horse,  and 
of  death  ;  and,  as  we  call  them  up  more  or  less  distinctly, 
there  is  a  kind  of  redness,  a  sort  of  offensiveness,  some  image 
of  a  horse,  and  some  appearance  of  mortality,  which  rises 
before  us.  And  should  we  be  asked,  Are  roses  red  ?  Has 
coal  gas  a  foul  smell  ?  Is  that  white  beast  a  horse }  Is  it 
true  that  he  is  dead  1  we  should  answer.  Yes,  our  ideas  are 
all  true,  and  are  attributed  to  the  reality.  But  the  idea  of 
redness  may  have  been  that  of  a  lobster,  of  a  smell  that  of 
castor-oil,  the  imaged  horse  may  have  been  a  black  horse, 
and  death  perhaps  a  withered  flower.  And  these  ideas  are 
not  true,  nor  did  we  apply  them.  What  we  really  applied 
was  that  part  of  their  content  which  our  minds  had  fixed  as 
the  general  meaning. 

*  I  may  point  out  that,  even  in  this  sense,  the  idea  is  a  product  of  abs- 
traction. Its  individuality  (if  it  has  such)  is  conferred  on  it  by  an  act  of 
thought.  It  is  given  in  a  congeries  of  related  phenomena,  and,  as  an 
individual  image,  results  from  a  mutilation  of  this  fact.  (Vid.  inf. 
Chap.  II.) 


lO  THE  PRINCIPLES  OF   LOGIC.  [Book  L 

It  may  be  desirable  (as  in  various  senses  various  writers 
have  told  us)  that  the  predicate  should  be  determinate,  but 
in  practice  this  need  can  not  always  be  satisfied.  I  may 
surely  judge  that  a  berry  is  poisonous,  though  in  what  way  I 
know  not,  and  though  "  poisonous  "  implies  some  traits  which  I 
do  not  attribute  to  this  poison.  I  surely  may  believe  that 
AB  is  bad,  though  I  do  not  know  his  vices,  and  have  images 
which  are  probably  quite  inapplicable.  I  may  be  sure  that  a 
book  is  bound  in  leather  or  in  cloth,  though  the  sort  of  leather 
or  cloth  I  must  imagine  I  can  not  say  exists.  The  details  I 
have  never  known,  or,  at  any  rate,  have  forgotten  them.  But 
of  the  universal  meaning  I  am  absolutely  sure,  and  it  is  this 
which  I  predicate. 

The  extreme  importance  of  these  obvious  distinctions 
must  excuse  the  inordinate  space  I  allot  to  them.  Our  whole 
theory  of  judgment  will  support  and  exemplify  them  ;  but  I 
will  add  yet  a  few  more  trivial  illustrations.  In  denying  that 
iron  is  yellow,  do  I  say  that  it  is  not  yellow  like  gold,  or 
topaze,  or  do  I  say  that  it  is  not  any  kind  of  yellow }  When 
I  assert,  "  It  is  a  man  or  a  woman  or  a  child,"  am  I  reasonably 
answered  by,  "  There  are  other  possibilities.  It  may  be  an 
Indian  or  a  girl "  }  When  I  ask,  Is  he  ill  }  do  I  naturally  look 
for  "  Oh  no,  he  has  cholera  "  }  Is  the  effect  of,  "  If  he  has  left 
me  then  I  am  undone,"  removed  by,  "  Be  happy,  it  was  by 
the  coach  that  he  deserted  you  "  ? 

The  idea  in  judgment  is  the  universal  meaning ;  it  is  not 
ever  the  occasional  imagery,  and  still  less  can  it  be  the  whole 
psychical  event. 

§  10.  We  now  know  what  to  understand  by  a  logical  idea, 
and  may  briefly,  and  in  anticipation  of  the  sequel,  dog- 
matically state  what  judgment  does  w^ith  it.  We  must  avoid, 
so  far  as  may  be,  the  psychological  and  metaphysical  dif- 
ficulties that  rise  on  us. 

^  Judgment  proper  is  the  act  which  refers  an  ideal  content 
(recognized  as  such)  to  a  reality  beyond  the  act.  This  sounds 
perhaps  much  harder  than  it  is. 

The  ideal  content  is  the  logical  idea,  the  meaning  as  just 
defined.  It  is  recognized  as  such,  when  we  know  that,  by 
itself,  it  is  not  a  fact  but  a  wandering  adjective.     In  the  act  of 


Chap.  L]        THE   GENERAL   NATURE   OF  JUDGMENT.  1 1 

assertion  we  transfer  this  adjective  to,  and  unite  it  with,  a  real 
substantive.  And  w^e  perceive  at  the  same  time,  that  the 
relation  thus  set  up  is  neither  made  by  the  act,  nor  merely 
holds  within  it  or  by  right  of  it,  but  is  real  both  independent 
of  and  beyond  it* 

If  as  an  example  we  take  once  more  the  sea-serpent,  we 
have  an  idea  of  this  but  so  far  no  judgment.  And  let  us 
begin  by  asking,  Does  it  e^^ist  .-^  Let  us  enquire  if  "it 
exists  "  is  really  true,  or  only  an  idea.  From  this  let  us  go 
on,  and  proceed  to  judge  "  The  sea-serpent  exists."  In  ac- 
complishing this  what  further  have  we  done  ?  And  the  answer 
is,  we  have  qualified  the  real  world  by  the  adjective  of  the 
sea-serpent,  and  have  recognized  in  the  act  that,  apart  from 
our  act,  it  is  so  qualified.  By  the  truth  of  a  judgment  we 
mean  that  its  suggestion  is  more  than  an  idea,  that  it  is  fact 
or  in  fact.  We  do  not  mean,  of  course,  that  as  an  adjective 
of  the  real  the  idea  remains  an  indefinite  universal.  The  sea- 
serpent,  if  it  exists,  is  a  determinate  individual ;  and,  if  we 
knew  the  whole  truth,  we  should  be  able  to  state  exactly  how 
it  exists.  Again  when  in  the  dusk  I  say.  That  is  a  quadruped, 
I  qualify  the  reality,  now  appearing  in  perception,  by  this 
universal,  while  the  actual  quadruped  is,  of  course,  much 
besides  four  legs  and  a  head.  But,  while  asserting  the  uni- 
versal, I  do  not  mean  to  exclude  its  unknown  speciality. 
Pa.tial  ignorance  need  not  make  my  knowledge  fallacious, 
unless  by  a  mistake  I  assert  that  knowledge  as  unconditional 
and  absolute. 

"  Are  the  angles  of  a  triangle  equal  to  two  right  angles  } " 
"  I  doubt  if  this  is  so."  "  I  affirm  that  this  is  so."  In  these 
examples  we  have  got  the  same  ideal  content ;  the  suggested 
idea  is  the  relation  of  equality  betv/een  the  angles  of  a 
triangle  and  two  right  angles.  And  the  affirmation,  or  judg- 
ment, consists  in  saying.  This  idea  is  no  mere  idea,  but  is  a 
quality  of  the  real.  The  act  attaches  the  floating  adjective  to 
the  nature  of  the  world,  and,  at  the  same  time,  tells  me  it  was 
there  already.     The  sequel,   I  hope,  may  elucidate  the  fore- 

*  I  may  remark,  that  I  am  dealing  at  present  only  with  affirmation  ;  the 
negative  judgment  presents  such  difficulties  that  it  can  hardly  be  treated 
by  way  of  anticipation. 


12  -  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

going,  but  there  are  metaphysical  problems,  to  which  it  gives 
rise,  that  we  must  leave  undiscussed. 

§  II.  In  this  description  of  judgment  there  are  two  points 
we  may  at  once  proceed  to  notice.  The  reader  will  have 
observed  that  we  speak  of  a  judgment  asserting  one  idea,  or 
ideal  content,  and  that  we  make  no  mention  of  the  subject 
and  copula.  The  doctrine  most  prevalent,  on  the  other  hand, 
lays  down  that  we  have  always  two  ideas,  and  that  one 
is  the  subject.  But  on  both  these  heads  I  am  forced  to 
dissent.  Our  second  chapter  will  deal  further  with  the 
question,  but  there  are  some  remarks  which  may  find  a  place 
here. 
f^"^  (i)  It  is  not  true  that  every  judgment  has  two  ideas.  We 
Y^may  say  on  the  contrary  that  all  have  but  one.  We  take  an 
ideal  content,  a  complex  totality  of  qualities  and  relations, 
and  we  then  introduce  divisions  and  distinctions,  and  we  call 
these  products  separate  ideas  with  relations  between  them. 
And  this  is  quite  unobjectionable.  But  what  is  objectionable, 
is  our  then  proceeding  to  deny  that  the  whole  before  our 
'  mind  is  a  single  idea;  and  it  involves  a  serious  error  in 
principle.  The  relations  between  the  ideas  are  themselves 
ideal.  They  are  not  the  psychical  relations  of  mental  facts. 
They  do  not  exist  between  the  symbols,  but  hold  in  the 
symbolized.  They  are  part  of  the  meaning  and  not  of  the 
existence.  And  the  whole  in  which  they  subsist  is  ideal,  and 
so  one  idea. 

Take  a  simple  instance.  We  have  the  idea  of  a  wolf  and 
we  call  that  one  idea.  We  imagine  the  wolf  eating  a  lamb, 
and  we  say.  There  are  two  ideas,  or  three,  or  perhaps  even 
more.  But  is  this  because  the  scene  is  not  given  as  a  whole  1 
Most  certainly  not  so.  It  is  because  in  the  whole  there  exist 
distinctions,  and  those  groupings  of  attributes  we  are  ac- 
customed to  make.  But,  if  we  once  start  on  this  line  and 
deny  the  singleness  of  every  idea  which  embraces  others,  we 
shall  find  the  wolf  himself  is  anything  but  one.  He  is  the 
synthesis  of  a  number  of  attributes,  and,  in  the  end,  we  shall 
find  that  no  idea  will  be  one  which  admits  any  sort  of  dis- 
tinction in  itself  Choose  then  which  you  will  say.  There  are 
no  single  ideas,  save  the  ideas  of  those  quaHties  which  are  too 


Chap.  I.]        THE   GENERAL   NATURE   OF  JUDGMENT.  1 3 

simple  to  have  afiy  distinguishable  aspects,  and  that  means 
there  are  no  ideas  at  all — or,  Any  content  whatever  the  mind 
takes  as  a  whole,  however  large  or  however  small,  however 
simple  or  however  complex,  is  one  idea,  and  its  manifold 
relations  are  embraced  in  an  unity.* 

We  shall  always  go  wrong  unless  we  remember  that  the 
relations  within  the  content  of  any  meaning,  however  complex, 
are  still  not  relations  between  mental  existences.    There  is  a 
wolf  and  a  lamb.     Does  the  wolf  eat  the  lamb  }  The  wolf  eats 
1the    lamb.     We  have    a  relation  here  suggested  or  asserted 
between  wolf  and  lamb,  but  that  relation  is  (if  I  may  use  the 
word)  not  a  factual  connection  between  events  in  my  head. 
,  What  is  meant  is  no  psychical  conjunction  of  images.     Just 
as  the  idea  of  the  wolf  is  not  the  whole  wolf-image,  nor  the 
idea  of  the  lamb  the  imagined  lamb,  so  the  idea  of  their  syn- 
thesis is  not  the  relation  as  it  exists  in  my  imagination.     In 
"the  particular  scene,  which  symbolizes  my  meaning,  there  are 
details  that  disappear  in  the  universal  idea,  and  are  neither 
thought  of  nor  enquired  after,  much  less  asserted. 
'       To  repeat  the  same  thing — the  imagery  is  a  sign,  and  the 
meaning  is  but  one  part  of  the  whole,  which  is  divorced  from 
the  rest  and  from  its  existence.     In  this  ideal  content,  there  are 
groups  and  joinings  of  qualities  and  relations,  such  as  answer  to 
nouns  and  verbs  and  prepositions.     But  these  various  elements, 
though  you  are  right  to  distinguish  them,  have  no  validity 
outside  the  whole  content.     That  is  one  idea,  which  contains 
all  ideas  which  you  are  led  tq  make  in  it ;  for,  whatever  is  fixed 
by  the  mind  as  one,  however  simple  or  complex,  is  but  one 
idea.     But,  if  this  is  so,    the  old  superstition  that  judgment 
\is  the  coupling  a  pair  of  ideas  must  be  relinquished. 

§  12.  I  pass  now  (ii)  to  the  other  side  of  this  error,  the 
doctrine  that  in  judgment  one  idea  is  the  subject,  and  that 
the  judgment  refers  another  to  this.     In  the  next  chapter  this 

*  The  psychological  controversy  as  to  the  number  of  ideas  we  can 
entertain  at  once,  can  hardly  be  settled  till  we  know  beforehand  what  is 
one  idea.  If  this  is  to  exclude  all  internal  complexity,  what  residuum  will 
be  left }  But,  if  it  admits  pluraHty,  why  is  it  one  idea  .^  If,  however, 
what  otherwise  we  should  call  plurality,  we  now  call  single  just  because  we 
have  attended  to  it  as  one,  the  question  must  clearly  alter  its  form. 


14  THE   PRINCIPLES  OF   LOGIC.  [Book  L 

view  will  be  finally  disposed  of,  but,  by  way  of  anticipation, 
we  may  notice  here  two  points,  {a)  Jh  "  wolf  eating  lamb  "  the 
relation  is  the  same,  whether  I  affirm,  or  deny,  or  doubt,  or 
ask.  It  is  therefore  not  likely  that  the  differentia  of  judgment 
will  be  found  in  what  exists  apart  from  all  judgment.  The 
differentia  will  be  found  in  what  differences  the  content,  as 
asserted,  from  the  content  as  merely  suggested. )  So  that,  if 
in  all  judgment  it  were  true  that  one  idea  is  the  subject  of  the 
assertion,  the  doctrine  would  be  wide  of  the  essence  of  the 
matter,  and  perhaps  quite  irrelevant.  But  {U)  the  doctrine 
(as  we  shall  see  hereafter)  is  erroneous.  "  B  follows  A," 
"A  and  B  coexist,"  "A  and  B  are  equal,"  "A  is  south  of  B  " 
— in  these  instances  it  is  mere  disregard  of  facts  which  can 
hold  to  the  doctrine.  It  is  unnatural  to  take  A  or  B  as  the 
subject  and  the  residue  as  predicate.  And,  where  existence 
is  directly  asserted  or  denied,  as  in,  "  The  soul  exists,"  or, 
"  There  is  a  sea-serpent,"  or,  "  There  is  nothing  here,"  the 
difficulties  of  the  theory  will  be  found  to  culminate. 

I  will  anticipate  no  further  except  to  remark,  that  in  every 
judgment  there  is  a  subject  of  which  the  ideal  content  is 
asserted.  But  this  subject  of  course  can  not  belong  to  the 
content  or  fall  within  it,  for,  in  that  case,  it  would  be  the  idea 
attributed  to  itself.  We  shall  see  that  the  subject  is,  in  the 
end,  no  idea  but  always  reality ;  and,  with  this  anticipation, 
we  must  now  go  forward,  since  we  have  finished  the  first 
division  of  this  chapter :  we  must  pass  from  the  general 
notion  of  judgment  to  the  criticism  of  certain  erroneous 
views,  a  criticism,  however,  which  is  far  from  exhaustive, 
and  in  some  points  must  depend  for  its  fuller  evidence  upon 
the  discussions  of  the  following  chapters. 

II.  §  13.  Wrong  theories  of  judgment  naturally  fall  into 
two  classes,  those  vitiated  by  the  superstition  of  subject 
predicate  and  copula,  and  those  which  labour  under  other 
defects.     We  will  take  the  last  first. 

(i)  Judgment  is  neither  the  association  of  an  idea  with  a 
sensation,  nor  the  liveliness  or  strength  of  an  idea  or  ideas. 
At  the  stage  we  have  reached,  we  need  subject  these  views  to 
no  detailed  examination.     The  ideas  which  they  speak  of  are 


Chap.  I.]        THE  GENERAL  NATURE  OF  JUDGMENT.  15 

psychical  events,  whereas  judgment,  we  have  seen,  has  to  do 
with  meaning,  an  ideal  content  which  is  universal,  and  which 
assuredly  is  not  the  mental  fact.  While  all  that  we  have  is  a 
relation  of"  phenomena,  a  mental  image,  as  such,  in  juxta- 
position with  or  soldered  to  a  sensation,  we  can  not  as  yet 
have  assertion  or  denial,  a  truth  or  a  falsehood.  We  have 
mere  reality,  which  is,  but  does  not  stand  for  anything,  and 
which  exists,  but  by  no  possibility  could  be  true. 

We  will  not  anticipate  the  general  discussion  of  "Asso- 
ciation "  (vid.  Book  II.  Part  II.  Chap.  I.),  and  will  pass  by 
those  extraordinary  views  the  school  holds  as  to  universals. 
We  will  come  at  once  to  the  result.  There  is  an  idea,  in  the 
sense  of  a  particular  image,  in  some  way  conjoined  with  or 
fastened  to  a  sensation.  I  have,  for  instance,  sensations  of 
coloured  points  ;  and  images  of  movement  and  hardness  and 
weight  are  "  called  up  "  by  these  sensations,  are  attracted  to, 
and  cohere  with  them.  And  this  sounds  very  well  till  we 
raise  certain  difficulties.  An  orange  presents  us  with  visual 
sensations,  and  we  are  to  add  to  these  the  images  just 
mentioned.  But  each  of  these  images  is  a  hard  particular, 
and  qualified  by  relations  which  exclude  it  from  all  others. 
If  you  simply  associate  this  bundle  of  facts,  who  would  take 
them  as  one  fact }  But  if  you  blend  their  content,  if,  neglecting 
the  existence,  you  take  a  part  of  the  quality  of  each,  and 
transfer  that  to  the  object,  then  you  may  call  your  process 
by  what  name  you  please,  but  it  certainly  is  not  association. 
(Vid.  infr.  Book  II.) 

But  let  us  suppose  that  the  ideas  are  united  somehow 
with  the  sensation,  yet  where  is  the  judgment,  where  is  truth 
or  falsehood  ?  The  orange  is  now  before  my  sense  or 
imagination.  For  my  mind  it  exists,  and  there  is  an  end  of 
it.  Or  say,  "  Caesar  will  be  angry."  Caesar  here  is  the  per- 
ception, which,  when  further  qualified,  becomes  "  Caesar  angry." 
But  this  image  again  is  simply  what  it  is,  it  does  not  stand  for 
anything,  and  it  can  mean  nothing. 

Let  us  suppose  in  the  first  place  that  the  "  idea  "  maintains 
itself,  then  no  doubt,  as  one  fact,  it  stands  in  mental  relation 
with  the  fact  of  the  sensation.  The  two  phenomena  coexist 
as     a   headache    may   coexist   with   a   syllogism ;    but   such 


i6  THE   PRINCIPLES  OF  LOGIC.  [Book  L 

psychical  coherence  is  far  from  assertion.  There  is  no  affirma- 
tion ;  and  what  is  there  to  affirm?  Are  we  to  assert  the 
relation  between  the  two  facts  }  But  that  is  given,  and  either 
to  assert  it  or  deny  it  would  be  senseless.*  Is  one  fact  to 
be  made  the  predicate  of  another  fact }  That  seems  quite 
unintelligible.  If  in  short  both  sensation  and  idea  are  facts, 
then  not  only  do  we  fail  to  find  any  assertion,  but  we  fail  to 
see  what  there  is  left  to  assert. 

But  in  the  second  place  (giving  up  association  proper)  let 
us  suppose  that  the  "  idea,"  as  such,  disappears,  and  that  its 
mutilated  content  is  merged  in  the  sensation.  In  this  case  the 
whole,  produced  by  blending,  comes  to  my  mind  as  a  single 
presentation.  But  where  is  the  assertion,  the  truth  or  false- 
hood ?  We  can  hardly  say  that  it  lies  in  the  bare  presentation 
itself  We  must  find  it,  if  anywhere,  in  the  relation  of  this 
presentation  to  something  else.  And  that  relation  would  be 
the  reference  of  judgment.  But  on  the  present  view  both  the 
something  else  and  the  reference  are  absent.  We  have  first 
an  unmodified  and  then  a  modified  sensation. 

The  only  way  to  advance  would  be  to  suppose,  in  the  first 
place,  that,  while  the  "  idea  "  maintains  itself,  it  is  distinguished 
from  its  content ;  and  to  suppose,  in  the  second  place,  that 
both  of  these  are  distinguished  from  the  sensation.  We  have 
then  two  facts,  a  sensation  and  an  image,  and  beside  these  a 
content  held  apart  from  the  image.  We  have  now  reached 
a  condition  which  would  make  judgment  possible,  but  the 
advance  to  this  condition  is  not  explicable  by  Association. 
Nor  could  the  further  steps  be  accounted  for.  You  have  the 
transference  of  the  content  from  the  image  to  the  sensation, 
and  the  qualification  of  the  latter  as  a  subject ;  but  both 
would  be  inexplicable.  We  may  add  that  it  is  impossible  for 
a  sensation  or  sensations  to  serve  as  the  subject  in  every 
judgment  (vid.  Chap.  II.).  And  finally  the  consciousness 
that,  what  my  act  joins,  is  joined  apart  from  it,  is  a  fact  not 
x:ompatible  with  the  psychology  we  are  considering.  To  sum 
up  the  whole-(7To  merge  the  content  of  an  image  in  a 
modified  presentation,  is  but  one  step  towards  judgment,  and 

*  We  might  say  that,  on  this  view,  the  denial  of  a  falsehood  must  ipso 
facto  be  false. 


Chap.  L]  THE  GENERAL   NATURE    OF  JUDGMEN^s,^  7- ; 


« 


it  is  a  very  long  step  beyond  association.     While  conjunctio 
or  coherence  of  psychical  phenomena  is  not  only  not  judgment, 
but  would  not  serve  as  its  earliest  basis  and  beginning.* 

§  14.  But  the  definition  I  shall  be  told  is  a  "  lively  idea 
associated  with  a  present  impression,"  and  I  shall  be  asked  if 
lively  makes  no  difference.  And  I  answer,  Not  one  particle  ; 
it  makes  no  difference,  even  if  you  suppose  it  true,  and  in 
addition  it  is  false.  The  liveliness  removes  none  of  the 
objections  we  have  been  developing.  Let  it  be  as  lively  as 
you  please,  it  is  a  mere  presentation,  and  there  is  no  judgment. 
The  liveliness  of  the  idea  not  only  is  not  judgment,  but  it  is 
not  always  even  a  condition.  The  doctrine  that  an  idea 
judged  true  must  be  stronger  than  one  not  so  judged,  will  not 
b^ar  confrontation  with  the  actual  phenomena.  You  may  go 
on  to  increase  an  idea  in  strength  till  it  passes  into  a  sensation, 
and  there  yet  may  be  no  judgment.  I  will  not  dwell  on  this 
point,  since  the  unadulterated  facts  speak  loudly  for  themselves, 
but  will  give  one  illustration.  We  most  of  us  have  at  times 
the  images  of  the  dead,  co-inhabitants  of  the  rooms  we  once 
shared  with  the  living.  These  images,  mostly  faint,  at  times 
become  distressing,  from  their  strength  and  particularity  and 
actual  localization  in  those  parts  of  the  room  which  we  do  not 
see.  In  an  abnormal  state  such  images,  it  is  well  known,  may 
become  hallucinations,  and  take  their  place  in  the  room  before 
our  eyes  as  actual  perceptions.  But  with  an  educated  man 
they  would  be  recognized  as  illusions,  and  would  not  be 
judged  to  be  outwardly  real,  any  more  than  the  fainter  and 
normal  images  are  judged  to  be  anywhere  but  in  our  own 
minds.  Yet  lively  ideas  associated  with  present  impressions 
— if  we  have  not  got  them  here,  where  are  they  } 

§  15.  We  turn  with  relief  from  the  refutation  of  a  doctrine, 

*  It  has  been  often  remarked  that,  on  Hume's  theory  of  belief,  there 
can  be  no  difference  between  imagination  and  reality,  truth  and  falsehood, 
and  that  why  we  make  this  difference  is  incomprehensible.  J.  S.  Mill 
with  great  openness  professed  on  this  head  the  total  bankruptcy  of  the 
traditional  doctrine.  He  seems  somehow  to  have  thought  that  a  complete 
break-down  on  a  cardinal  point  was  nothing  against  the  main  doctrine  of 
his  school,  nor  anything  more  than  a  somewhat  strange  fact.  It  was  im- 
possible that  he  should  see  the  real  cause  of  failure.  We  shall  deal  with 
Professor  Bain's  views  lower  down. 

C 


1 8  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

long  dead  and  yet  stubbornly  cumbering  the  ground,  to 
consider  a  fresh  error,  the  confusion  of  judgment  with 
practical  belief.  I  cannot  enquire  how  far  any  psychical 
activity  is  consistent  with  the  theory  of  Professor  Bain,  nor 
can  I  discuss  the  nature  of  a  psychical  activity  which  seems 
physiologically  to  consist  in  muscular  innervation  ;  though  I 
am  bound  to  add  that  (doubtless  owing  to  my  ignorance) 
Professor  Bain's  physiology  strikes  me  here  as  being  as- 
tonishingly misty.  And  I  must  pass  by  the  doubt  whether, 
if  we  accept  his  view,  we  shall  find  the  confusion  between 
image  and  meaning  in  any  way  lessened. 

We  must  remember  that  the  question.  Is  judgment  always 
practical,  does  not  mean.  Is  the  will  in  any  way  concerned  in 
it.  In  that  case  it  might  be  argued  that  all  generation  of 
psychical  phenomena  comes  under  the  head  Will.  The 
question  means.  Does  the  essence  of  judgment  lie,  not  in  the 
production  of  truth  and  falsehood — states  which  alter  nothing 
in  the  things  they  represent — but  rather  in  the  actual  produc- 
tion of  a  change  in  real  existence.  Or,  more  simply,  when  an 
idea  is  judged  to  be  true,  does  this  mean  that  it  moves  some 
other  phenomenon,  and  that  its  assertion  or  denial  is  nothing 
but  this  motion  t  The  doctrine  admits  that  an  idea  or  ideas, 
when  held  true,  differ  vitally  from  the  same  when  suggested  ; 
and  it  proceeds  to  assert  that  the  differentia  is  the  effect  of  the 
idea  on  our  conduct,  and  that  there  is  no  other  differentia  at  all. 

There  is  a  logical  mistake  we  may  point  out  before  pro- 
ceeding, for  it  is  the  error  which  has  led  Professor  Bain  astray. 
Assume  that  an  asserted  idea  causes  action,  and  that  an  idea, 
not  believed  in,  does  not  influence  conduct.  From  these 
premises  can  we  conclude.  Therefore  judgment  is  influence  ? 
If,  in  other  words,  when  A  changes  to  B,  we  have  an  unfailing 
difference  q,  and  q  is  not  found  except  after  A,  does  this 
warrant  the  assertion,  that  the  alteration  consists  in  q }  Is  it" 
not  quite  possible  that  q  follows  from  /,  and  that  /  is  what 
really  turns  A  into  B  .?  We  shall  do  well  to  keep  our  eye  on 
this  logical  fallacy,  ^he  assertion  we  are  to  examine  is  not 
that  practical  influence  induces  us  to  judge,  or  results  from  a 
judgment :  What  is  asserted  is  that  judgment  is  nothing  else 
whatever.    \ 


Chap.  1.]    THE  GENERAL  NATURE  OF  JUDGMENT.       1 9 

Against  this  false  differentia  I  shall  briefly  maintain,  {a) 
that  the  differentia  may  be  absent  from  the  fact,  ip)  that  it 
may  be  present  with  other  facts,  (c)  that  the  fact  contains 
other  characteristics,  which  are  the  true  differentia,  and  are 
absent  from  the  false  one,  {d)  that  the  latter  has  a  positive 
quality  which  excludes  the  fact. 

(a)  If  we  test  the  theory  by  abstract  instances  such  as, 
The  angles  of  a  triangle  are  equal  to  two  right  angles,  it 
collapses  at  once.  It  is  impossible  to  find  always  a  practical 
influence  exerted  by  the  ideas.  We  may  be  answered  "  But 
they  might  exert  it,  you  surely  would  act  on  them."  And 
such  an  answer  may  pass  in  the  school  of  "  Experience  ; "  but 
a  poor  "  transcendentalist "  will  perhaps  be  blamed  if  he 
usurps  such  a  privilege.  He  at  least  is  not  allowed  to  take 
tendency  and  possibility  and  mere  idea  for  fact.  And  he  can 
hardly  be  prevented  from  pressing  the  question.  Is  the  influence 
there  or  not  1  If  it  is  not  there,  then  either  Professor  Bain's 
theory  disappears,  or  he  should  alter  his  definition,  and  say 
that  an  idea  passes  into  a  judgment  when  enriched  by  poten- 
tialities and  eventual  tendencies.  If  these  are  not  ideas  we 
should  be  told  what  they  are  ;  but  if  they  are  only  ideas  that 
go  with  the  first  ideas,  then  our  answer  is  plain.  In  the  first 
place  it  is  not  true  that  they  are  always  there  :  in  the  second 
place  it  is  not  true  that,  when  added,  they  must  exert  a 
practical  influence. 

{h)  In  the  second  place  ideas  may  influence  me,  though  I 
never  do  hold  them  for  true.  The  feelings  and  emotions 
associated  with  an  idea  can  often  prevent  or  produce  volitions, 
although  the  idea  is  not  affirmed  as  true,  and  even  while  it  is 
recognized  as  false.  Though  I  do  not  believe  that  a  slow- 
worm  can  bite,  or  a  drone  can  sting,  I  may  shrink  from 
touching  them.  I  may  avoid  a  churchyard  though  I  believe 
in  no  ghosts.  An  illusion  no  doubt,  if  recognized  as  such, 
does  not  influence  volition  either  so  much,  or  always  in  the 
same  way ;  but  still  it  may  operate  in  spite  of  disbelief.* 
And  it  can  hardly  be  a  true  view  which  forces  us  to  say,  If 

*  It  maybe  said  that  when  it  operates  the  denial  is  suspended.  But  I 
confess  I  can  find  no  ground  for  such  a  statement.  At  any  rate  it  is 
certain  that  the  idea  can  operate  though  a  positive  judgment  is  not  there. 

C   2 


20  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

you  judged  it  an  illusion  you  would  wholly  disregard  it,  for 
such  disregard  ts  judgment. 

I  will  not  dwell  on  a  point  it  would  be  easy  to  illustrate. 
In  passing,  however,  I  may  remind  the  reader  of  that  class  of 
ideas  which  influences  our  actions  without  seeniing  to  be  true. 
I  refer  to  practical  ideas,  the  representation  of  a  satisfied 
desire  which  is  now  felt  to  be  unsatisfied.  It  is  certain  that 
these  move  us  to  active  pursuit,  and  it  is  equally  certain  they 
are  not  judged  to  be  real ;  for  if  they  were,  then  for  that 
reason,  they  would  fail  to  move  us.* 

(c)  But  suppose  that  all  judgment  did  really  move  to 
action.  Would  this  show  that  judgment  was  nothing  but 
such  motion  .?  Most  certainly  not  so.  We  can  observe  what 
takes  place  in  us,  when  a  suggested  idea  is  judged  to  be 
true ;  and  clearly  an  activity  (however  hard  to  describe)  does 
show  itself  there,  and  yet  is  not  directed  (except  per  accidens) 
towards  making  a  change  in  the  world  and  in  ourselves. 
And  if  this  true  dijferentia  can  be  verified,  that  should  settle 
the  question.  And  again,  apart  from  direct  observation,  we 
can  argue  indirectly.  Assertion  and  denial,  together  with  the 
difference  of  truth  and  falsehood,  are  real  phenomena,  and 
there  is  something  in  them  which  falls  outside  the  influence  of 
ideas  on  the  will.  It  is  comic  if  the  judgment.  It  will  rain 
to-morrow,  is  the  same  as  buying  an  umbrella  to-day  ;  or, 
Put  on  your  thick  boots,  is  a  truer  form  of.  It  rained  hard 
yesterday.  And  when  a  child  sees  a  berry  and,  as  we  say, 
judges.  It  made  me  sick  before,  it  seems  strange  that  the  act 
of  affirmation  should  consist  in  practical  abstention  to-day 
and  should  be  nothing  else. 

(d)  And  not  only  are  the  genuine  characteristics  absent 
from  a  mere  practical  attitude,  but  we  find  present  there  a 
quality  which  is  absent  from  real  judgment.  The  truth  of  a 
suggestion  is  not  a  matter  of  degree,  and  the  act  which 
attributes  an  idea  to  reality  either  refers  it,  or  does  not  refer 
it.  It  can  hardly  do  either  a  little  more  or  less  and  to  a 
certain  degree  (cf.  Chap.  VII.).  In  strictness  of  speech  all 
halt-truths  are  no  truths,  and,  "  It  is  more  or  less  true,"  really 

*'  I  may  refer  on  this  point  to  my  Ethical  Studies,  Essay  VH. 


Chap.  I.]  THE   GENERAL   NATURE   OF  JUDGMENT.  21 

means,  "  It  is  true  with  a  qualification,"  or  "  More  or  less  of  it 
is  true,  though  as  a  whole  it  is  not  true."  But  the  practical 
influence  of  ideas  must  have  degree,  and  so  possess  a  quality 
which  judgment  has  not. 

For  these  reasons,  each  of  which  can  stand  almost  alone, 
it  seems  clear  that  the  doctrine  before  us  has  failed.     And 
one  cause  of  the  error  seems  to  lie  in  the  neglect  of  some 
important  distinctions  we  may  proceed  to  notice.     Judgment 
is  primarily  logical,  and  as  such  has  no  degrees  ;  the  relation 
of  the  ideal   content  to  reality  must  be  there  or  not  there. 
Belief,  on   the   other   hand,   is    primarily  psychological,  and, 
whether  theoretic  or  practical,  exists  in  a  degree,     (a)  Intel- 
lectual belief  or  conviction  is  the  general  state  which  corre- 
sponds to  the  particular  acts  of  judgment.     To  believe  that  A 
is  B  may  mean  that,  whenever  the  idea  A-B  is  suggested,  I  go 
on  to  affirm  it ;  or,  further,  that  the  idea  fills  much  space  in 
my  mind,  is   a  persistent  habit  and   ruling  principle,  which 
dominates  my  thoughts  and  fiills  my  imagination,  so  that  the 
assertion  A-B   is  frequently  made  and  has  wide  intellectual 
ramifications  and  connections.    I  should  believe  A-B  less,  if  it 
more  seldom  arose,  by  itself  or  by  implication,  and  had  in- 
ferior influence.     I  should  believe  less  still  if,  when  A-B  was 
suggested,  I  sometimes  doubted  it ;  and  even  less,  if  I  affirmed 
it  more  seldom,  and  then  with  hesitation,  against  doubts,  and 
with  inability  to  maintain  the  attitude.     On  the  other  hand  I 
should  not  believe  at  all,  if  I  only  were  more  or  less  convinced, 
perceiving  more  or  less  reason  on  both  sides,  inclined  in  one 
direction,  but  unable  to  cross  the  line  and  to  affirm,     (d)  But 
in  practical  belief,  beside  these  degrees  of  intellectual  convic- 
tion, there  is  another  element  of  more  and  less.     Not  only  is 
the  truth  of  the  intellectual  content  more  or  less  present,  but 
in  addition  it  can  influence  my  will  more  or  less.     A  desire 
stronger  or  more  persistent,  or  more  dominant  generally,  may 
answer  to  it  on   the  one  side,  or  on  the  other  a  weaker  and 
more  fleeting  impulse.     Beside  existing  more  or  less,  it  can 
move  more  or  less.     It  is,  I  think,  not  easy  to  keep  clear  of 
confusion  unless  these  ambiguities  are  noticed   and  avoided. 
But  the  main  logical  mistake  which  Professor  Bain  has  com- 
mitted   is   to   argue   from   the  (false)  premise,  "Belief  must 


22  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

induce  action  "  to  the  inconsequent  result  "  Belief  is  that  in- 
ducement."* 

§  1 6.  (ii)  Leaving  now  the  first  group  of  erroneous  views 
we  may  proceed  to  consider  another  collection.  These  may 
be  classed  as  labouring  under  a  common  defect,  the  false 
notion  that  in  judgment  we  have  a  pair  of  ideas.  We  were 
engaged  with  this  fallacy  in  §  ii,  and  it  will  meet  us  again  in 
the  following  chapter,  so  that  here  some  brief  remarks  may 

!  suffice.  In  their  ordinary  acceptation  the  traditional  subject, 
predicate,  and  copula  are  mere  superstitions.  The  ideal 
matter  which  is  affirmed  in  the  judgment,  no  doubt  possesses 
internal  relations,  and  in  most  cases  (not  all)  the  matter  may 
be  arranged  as  subject  and  attribute.  But  this  content,  we 
have  seen,  is  the  same  both  in  the  assertion  and  out  of  it.  If 
you  ask  instead  of  judging,  what  is  asked  is  precisely  the 
same  as  what  is  judged.  So  that  it  is  impossible  that  this 
internal  relation  can  itself  be  the  judgment ;  it  can  at  best  be 
no  more  than  a  condition  of  judging.  We  may  say  then,  if 
the  copula  is  a  connection  which  couples  a  pair  of  ideas,  it 
falls  outside  judgment ;  and,  if  on  the  other  hand  it  is  the  sign 
of  judgment,  it  does  not  couple.  Or,  if  it  both  joined  and 
judged,  then  judgment  at  any  rate  would  not  be  mere  joining. 
I  will  dwell  here  no  more  on  the  general  error.  We  shall 
see  its  effects  in  some  mistaken  views  we  may  proceed  to 
notige. 
/"     (a)  Judgment   is   not  inclusion  in,  or  exclusion  from,   a 

V  class.  The  doctrine  that  in  saying,  "  A  is  equal  to  B,"  or  "  B  is 
to  the  right  of  C,"  or  "  To-day  precedes  Monday,"  I  have  in 
my  mind  a  class,  either  a  collection  or  a  description^  of  "  things 

*  In  the  third  edition  of  his  Emotions  (1875)  P^'of  Bain  apparently 
reconsiders  the  question,  but  I  can  neither  tell  if  he  abandons  his  theory, 
nor  what  it  is  that,  if  so,  he  puts  in  its  place.  As  I  am  entirely  unable  to 
understand  this  last  theory,  my  remarks  must  be  taken  to  apply  to  the 
earlier  one.  Since  this  volume  was  written  I  have  made  acquaintance 
with  Mr.  Sully's  criticism  on  Prof.  Bain's  doctrine  {^Sensation  and 
Intuition.  2nd  ed.  1880).  But  he^  I  find,  treats  Prof.  Bain's  third 
edition  (1875),  in  which  an  earher  edition  of  his  own  criticism  is  treated 
with  the  greatest  respect,  as  if  it  either  had  no  existence,  or  at  all  events 
was  somehow  irrelevant  to  the  issue.  For  myself  I  must  say  that  for  the 
reason  given  above  I  confine  myself  to  the  earlier  theory. 


Chap.  L]  THE  GENERAL   NATURE   OF  JUDGMENT.  23 

equal  to  B,"  or  "  to  the  right  of  C,"  or  "  preceding  Monday,"  is 
quite  opposed  to  fact.  It  is  as  absurd  as  the  assertion  that, 
in  "  It  is  our  son  John,"  or  "  It  is  my  best  coat,"  or  "9  =  7  +  2,"  I 
think  of  a  class  of  "  our  sons  John,"  or  "  my  best  coats,"  or 
"that  which  is  equal  to  7  +  2."  If  the  view  stood  apart  from 
implied  preconceptions,  and  by  itself  as  an  interpretation  of 
fact,  it  would  scarcely,  I  think,  be  so  much  as  discussed. 
And,  as  we  shall  be  forced  to  recur  to  it  hereafter  (Chap.  VI.), 
we  may  so  leave  it  here. 

{b)  Judgment  is  not  inclusion  in,  or  exclusion  from,  the 
subject.  By  the  subject  I  mean  here  not  the  ultimate 
subject,  to  which  the  whole  ideal  content  is  referred,  but  the 
subject  which  lies  within  that  content,  in  other  words  the 
grammatical  subject.  In  "  A  is  simultaneous  with  B,"  "  C  is 
to  east  of  D,"  "  E  is  equal  to  F,"  it  is  unnatural  to  consider 
A,  C,  and  E  as  sole  subjects,  and  the  rest  as  attributive.  It  is 
equally  natural  to  reverse  the  position,  and  perhaps  rriore 
natural  still  to  do  neither,  but  to  say  instead,  "A  and  B  are 
synchronous,"  "  C  and  D  lie  east  and  west,"  "  E  and  F  are 
equal."  The  ideal  complex,  asserted  or  denied,  no  doubt  in 
most  cases  will  fall  into  the  arrangement  of  a  subject  with 
adjectival  qualities,  but  in  certain  instances,  and  those  not  a 
few,  the  content  takes  the  form  of  two  or  more  subjects  with 
adjectival  relations  existing  between  them.  I  admit  you  may 
torture  the  matter  from  the  second  form  into  the  first,  but,  if 
torture  is  admitted,  the  enquiry  will  become  a  mere  struggle 
between  torturers.  It  requires  no  great  skill  to  exhibit  every, 
subject  together  with  its  attributes  as  the  relation  between 
independent  qualities  (subjects),  or  again  even  to  make  that 
relation  the  subject,  and  to  predicate  all  the  remainder  as  an 
attribute.  Thus,  in  "  A  is  simultaneous  with  B,"  it  is  as  easy 
to  call  "exists  in  the  case  of  AB"  an  attribute  of  simultaneity, 
as  it  is  to  call  "  simultaneous  with  B  "  an  attribute  of  A.  We 
may  finally  observe  that  existential  judgments  do  not  lend 
themselves  easily  to  the  mistake  we  are  considering.  And 
such  negative  judgments  as  "  Nothing  is  here,"  will  be  found 
hard  to  persuade.  But  on  both  these  points  I  must  refer  to 
the  sequel  (Chaps.  II.  and  III.). 

(c)  Judgment    is     not    the    assertion    that    subject    and 


24  THE   PRINCIPLES  OF   LOGIC.  [Book  L 

predicate  are  identical  or  equal.  This  erroneous  doctrine  is 
the  natural  result  of  former  errors.  You  first  assume  that  in 
judgment  we  have  a  relation  between  two  ideas,  and  then  go 
on  to  assume  that  these  ideas  must  be  taken  in  extension. 
But  both  assumptions  are  vicious  :  and,  if  we  consider  the 
result,  asking  not  if  it  is  useful  but  whether  it  is  true,  we  can 
hardly,  I  think,  remain  long  in  hesitation.  That  in  "  You  are 
standing  before  me,"  or  "  A  is  north  of  C,"  or  "  B  follows  D," 
what  we  really  mean  is  a  relation,  either  of  equality  or 
identity,  is  simply  incredible  :  and  torture  of  the  witness  goes 
to  such  lengths  that  the  general  public  is  not  trusted  to 
behold  it* 

However  useful  within  limits  the  equation  of  the  terms 
may  be  found,  if  you  treat  it  as  a  working  hypothesis  (vid. 
Book  II.  Part  II.  Chap.  IV.),  yet  as  a  truth  it  will  not  bear  any 
serious  examination.     Let  us  look  at  it  more  closely. 

(i)  If  what  is  asserted  be  equality,  then  that  of  course  is 
identity  in  quantity,  and  is  nothing  else  whatever.  And  I 
must  venture  to  complain  of  the  reckless  employment  of  this 
term.  To  use  the  sign  =  for  qualitative  sameness,  or  for 
individual  identity  (I  do  not  ask  here  if  these  are  different),  is 
surely  barbarous.  No  harm  perhaps  may  come,  but  there 
should  be  some  limit  to  the  abuse  and  confusion  we  allow 
ourselves  in  practice.  Let  us  then  first  take  equality  in  its 
proper  sense,  to  stand  for  an  identity  in  respect  of  quantity. 
But,  if  so,  if  the  subject  and  predicate  are  equated,  if  "  Negroes 
are  men,"  when  written  "All  negroes  =  some  men,"  is  on  a 
level  with  2=12  —  10 — if  what  is  said  and  signified  is  that 
between  the  terms,  if  you  compare  them  numerically,  there  is 
no  difference  whatever,  we  can  at  once  pass  on.  It  is  certain 
that  j'^;;^^  judgments,  at  least,  can  not  express  this  relation  of 
quantity,  and  it  is  certain  again  that,  of  those  which  can,  it  is 
only  a  very  small  class  which  do.  Illustration  is  hardly 
wanted.  "  Hope  is  dead  "  would  mean  that,  "  In  hope  and  a 
fraction  of  dead  things  there  is  exactly  the  same  sum  of 
units."  And,  in  asserting  that  "Judgment  is  not  an  equation,"  I 
should  express  my  belief  that  to  divide  both  by  2  would  not 
give  the  same  quantity. 

*  Vid.  Jevons,  Principles  of  Science,  Chap.  I.  §  12. 


Chap.  I.]  THE   GENERAL   NATURE   OF  JUDGMENT.  25 

But  the  sign  =  does  not  seem  to  mean  equality.  It  does 
not  mean  that  the  units  of  the  subject  and  predicate  are  iden- 
tical in  qna7itity.  It  would  appear  to  mean  that  they  are  the 
same  altogether.  The  identity  it  asserts  is  not  quantitative, 
but  seems  absolute.  In  "  All  Negroes  =  some  men,"  the  "  =  " 
represents  exclusion  of  difference  both  quantitative  and 
qualitative. 

(ii)  The  identity  is  {a)  not  likeness  :  it  is  not  a  relation 
consisting  in  a  partial  qualitative  identity,  definite  or  in- 
definite. "  Iron  =  some  metal "  can  hardly  mean  "  Some  metal 
is  similar  to  iron."  Not  only  do  the  facts  exclude  this  inter- 
pretation, but  the  theory  would  not  work  with  it.  If 
"  similars "  and  "  likeness  "  are  phrases  that  occur,  this  is  a 
proof  that  here,  as  in  the  case  of  =,  the  theory  does  not 
mean  what  it  says,  or  quite  know  what  it  is  doing.  That 
when  A  is  like  B  you  may  write  one  for  the  other,  is  of  course 
quite  untrue  (cf.  Book  II.). 

(b)  The  identity  again  is  not  definitely  partial,  consisting 
in  sameness  in  some  particular  point  or  points  of  quality. 
For,  on  this  interpretation,  you  could  make  no  advance,  until 
the  point  of  sameness  had  been  specified.  And  even  then 
the  equational  theory  would  not  work. 

(c)  Unless  we  suppose  that  both  sides  differ  only  in  name, 
and  that  this  difference  of  names  is  the  import  of  the 
judgment — a  view  we  shall  glance  at  in  a  future  chapter 
(Chap.  VI.) — we  must  take  the  sign  =  to  mean  total  same- 
ness to  the  exclusion  of  all  difference.  But,  if  so,  the  theory 
must  reform  itself  at  once,  if  it  desires  to  be  consistent.  It 
will  not  be  true  that  "  Negroes  =  some  men,"  for  certainly 
"  some  men  "  are  not  "  =  negroes."      Nor  again  will  it  be  true 

.that  negroes  are  equal  to  a  certain  stated  fraction  of  mankind. 
That  stated  fraction  is  an  universal  adjective  which  might  be 
applicable  to  other  men  as  well  as  to  negroes.  If  "  is  "  or  "  =  " 
stands  for  "  is  the  same  as,"  then  it  is  as  false  to  say  "  A  is  ^B  " 
as  it  was  before  to  say  "A  is  some  B."  "  Some  B  "  covers  not 
only  the  B  which  is  A :  it  may  hold  just  as  much  of  the  other 
B,  which  we  take  as  not- A.  And  it  is  sowith"iB":  that 
applies  just  as  much  to  the  §  which  are  not- A,  as  it  does  to 
the  third  which  is  identical  with  A.     The  quantification  of  the 


26  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

predicate  is  a  half-hearted  doctrine,  which  runs  against  facts, 
if  "  =  "  does  mean  equal/is  ridiculous  if  "  ="  comes  to  no  more 
than  plain  "  is,''  and  is  downright  false  if  "  =  "  stands  for  "  is 
the  same  asT 

To  be  consistent  we  must  not  merely  quantify  the 
predicate,  we  must  actually  specify  it.  The  men  that  are 
negroes  are  not  any  and  every  set  of  men,  who  have  a  certain 
number.  They  are  those  men  who  are  negroes,  and  this  is 
the  predicate.  Negroes  =  negro-men,  and  iron  =  iron-metal. 
The  predicate  now  really  and  indeed  seems  the  subject,  and 
can  be  substituted  for  it.  The  idea  is  a  bold  one,  and  its 
results  have  been  considerable  ;  but  if  we  look  not  at  working 
power  but  at  truth,  the  idea  is  not  bold  enough,  and  wants 
courage  to  remove  the  last  contradiction. 

That  A  should  be  truly  the  same  as  AB,  and  AB  entirely 
identical  with  A,  is  surely  a  somewhat  startling  result.  If 
A  =  A,  can  it  also  be  true  that  to  add  B  on  one  side  leaves  the 
equation  where  it  was  }  If  B  does  not  mean  o,  one  would  be 
inclined  to  think  it  must  make  some  difference.  But,  if  it 
does  make  a  difference,  we  can  no  longer  believe  that  A  =  AB, 
and  AB  =  A.  If  "  iron-metal  "  is  the  same  as  "  iron,"  how  mis- 
leading it  is  to  set  down  the  two  sides  as  different  terms.  If 
there  really  is  a  difference  between  the  two,  then  your  statement 
is  false  when  by  your  "  =  "  you  deny  it.  But  if  there  is  no 
difference,  you  are  wrong  in  affirming  it,  and  in  opposing 
"  iron  "  to  "  iron-metal." 

There  is  only  one  issue.  If  A  is  AB,  then  the  A  that  is 
AB  is  not  A  but  — AB.  Both  sides  of  the  assertion  are  just 
the  same,  and  must  be  so  stated.  Negro-men  are  negro-men, 
and  iron-metal  is  iron-metal.*  For  consider  the  dilemma. 
B  either  is  or  is  not  an  addition  to  A.  If  it  is  not  an  addition, 
its  insertion  is  gratuitous ;  it  means  nothing  on  either  side, 
may  fall  upon  whichever  side  we  choose,  is  absurd  on  both 
alike,  and  should  be  got  rid  of — then  A  =  A.  But  if  B  is  an 
addition,  then  A  =  AB  cannot  be  true.  We  must  add  B  on 
both  sides,  and  AB  =  AB.  In  short  B  must  disappear  or 
have  a  place  on  each  side. 

We  have  now  reached  consistency,  and  the  reader  may 
*  Cf.  Lotze,  Logik,  80-2. 


Chap.  L]  THE   GENERAL   NATURE   OF  JUDGMENT.  27 

ask,  Is  the  result  still  false  ?  I  do  not  like  to  seem  obstinate, 
and  I  prefer  to  reply.  Do  you  think  it  is  true  ?  I  will  accept 
your  answer.  If  you  say  that  identical  propositions  are  all 
false,  I  shall  not  contradict  you  (cf.  Chap.  V.  §  i),  for  I  also 
believe  that  a  judgment  which  asserts  no  difference  is 
nothing.  But  if  you  pronounce  on  the  side  of  truth,  I  should 
like  to  ask  a  question.  For  an  assertion  to  be  true  must  it 
not  assert  something,  and  what  is  it  that  you  take  to  be 
asserted  above  .?  That  where  there  is  no  difference,  there  is 
no  difference,  that  AB  will  be  AB  as  long  as  it  is  AB  ?  You 
can  hardly  mean  that.  Is  the  existence  of  AB  what  is  secretly 
asserted  ?  But,  if  so,  we  should  say  openly  "  AB  exists,"  and 
our  reduplication  of  AB  is  surely  senseless.  We  know  that  it 
exists,  not  because  we  double  it,  but,  I  suppose,  because  we 
know  of  its  existence. 

But  what  then  do  we  assert  by  AB  =  AB  }  It  seems 
we  must  own  that  we  do  not  assert  anything.  The  judg- 
ment has  been  gutted  and  finally  vanishes.  We  have 
followed  our  premises  steadily  to  the  end,  and  in  the  end 
they  have  left  us  with  simply  nothing.  In  removing  the 
difference  of  subject  and  predicate  we  have  removed  the 
whole  judgment* 

§  17.  'We  have  seen  the  main  mistakes  of  the  foregoing 
doctrines.  It  is  a  more  pleasing  task  to  consider  the  main 
truth  which  each  one  of  them  has  seized,  (i)  The  views  we 
began  to  criticize  in  §  13,  have  avoided  the  error  of  subject 
predicate  and  copula.  They  have  seen  that  in  judgment  the 
number  of  ideas  is  not  the  main  question,  and  that  the 
essence  of  the  matter  does  not  lie  in  the  ideas,  but  in  some- 

*  It  is  not  worth  while  to  criticize  in  detail  a  doctrine  we  can 
show  is  fallacious  in  principle.  Cf.  Chap.  VI.  But  among  minor  objec- 
tions to  the  quantification  of  the  predicate  is  its  claim  to  silence  you,  and 
prevent  you  from  saying  what  indubitably  you  know.  It  tells  you  you 
must  not  say  "  A  is  B,"  unless  you  also  certify  how  much  of  B  is  A.  But, 
even  supposing  that  "  so  much  of  B  "  is  the  truth  that  you  would  affirm  if 
you  could,  in  numerous  cases  you  can  not  affirm  it.  You  know  that  A 
possesses  a  quality  B,  and,  as  to  how  the  B,  that  is  A,  stands  in  extent  to 
the  B  which  is  not  A,  you  have  no  information.  You  must  either  then 
decline  to  quantify,  or  must  abstain  from  speaking  the  truth  you  know. 
But  it  is  not  worth  while  to  criticize  in  detail. 


28  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

thing  beyond  them.  Nor,  to  be  more  particular,  is  the 
implication  of  will  in  all  judgment  a  complete  mistake.  It  is 
true  that,  in  an  early  stage  of  developement,  the  intelligence  is 
so  practical  that  it  hardly  can  be  said  to  operate  indepen- 
dently. It  is  true  again  that,  in  the  evolution  of  self-con- 
sciousness, the  opposition  of  idea  and  reality  depends,  to  a 
degree  I  will  not  here  discuss,  upon  volitional  experience. 
And  in  these  points  there  is  truth  in  the  theory,  which, 
however  much  he  may  abandon  it,  we  shall  place  to  the  credit 
of  Professor  Bdin.  And  the  view  that  in  judgment  we  have 
an  association  of  idea  with  sensation,  and  a  coalescence  of  both 
elements,  is  far  from  being  wholly  destitute  of  truth.  For 
(as  we  shall  see  in  the  following  Chapter)  the  subject  in  all 
judgment  is  ultimately  the  real  which  appears  in  perception  : 
and  again  it  holds  good  that  the  lowest  stage,  in  the  develope- 
ment of  judgment  and  inference  alike,  is  the  redintegration 
of  ideal  elements  with  sensuous  presentation,  in  such  a 
manner  that  the  two  are  not  distinguished,  but  run  into  one 
whole. 

(ii)  And  from  the  second  class  of  errors  we  may  also 
collect  important  results.  In  the  first  place  it  is  true  that  the 
content  asserted  is  always  complex.  It  can  never  be  quite 
simple,  but  must  always  involve  relations  of  elements  or 
distinguishable  aspects.  And  hence,  after  all,  in  judgment 
there  must  be  a  plurality  of  ideas.  And,  in  particular,  {a) 
though  it  is  false  that  the  predicate  is  a  class  in  which  the 
subject  is  inserted,  and  a  fundamental  error  to  take  the 
universal  in  the  form  of  a  collection,  yet  it  is  entirely  true 
that  the  predicate  must  be  always  an  universal.  For  every 
idea,  without  exception,  is  universal.  And  again  {b)  though 
assertion  is  not  attribution  to  a  subject  in  the  judgment, 
though  it  is  false  that  the  grammatical  subject  is  the  reality  of 
which  the  predicate  is  held  true,  yet  in  every  judgment  there 
must  be  a  subject.  The  ideal  content,  the  adjective  divorced, 
is  made  real  once  again  by  union  with  a  substantive.  And 
(c)  the  doctrine  of  equation,  or  identity  of  the  terms,  has 
itself  grasped  a  truth,  a  truth  turned  upside  down  and  not 
brought  to  the  light,  but  for  all  that  a  deep  fundamental 
principle. 


Chap.  I.]  THE  GENERAL   NATURE   OF  JUDGMENT.  29 

Turned  upside  down,  and  made  false,  it  runs  thus.  The 
object  of  judgment  is,  despite  their  difference  in  meaning,  to 
assert  the  identity  of  subject  and  predicate  when  taken  in 
extension.  But  turned  the  right  way  up  it  runs  thus.  The 
object  of  judgment  is,  under  and  within  the  identity  of  a 
subject,  to  assert  the  synthesis  of  different  attributes.  When- 
ever we  write  "  =  "  there  must  be  a  difference,  or  we  should 
be  unable  to  distinguish  the  terms  we  deal  with  (cf  Chap.  V.). 
And  when  a  judgment  is  turned  into  an  equation,  it  is  just 
this  difference  that  we  mean  to  state.  In  "  S  =  P  "  we  do 
not  mean  to  say  that  S  and  P  are  identical.  We  mean  to  say 
that  they  are  different,  that  the  diverse  attributes  S  and  P  are 
united  in  one  subject ;  that  S  —  P  is  a  fact,  or  that  the 
subject  S  is  not  bare  S,  but  also  S  —  P.  And  the  reason  why 
the  theory  of  equation  works,  and  is  not  mere  nonsense,  is 
that  in  fact  it  is  an  indirect  way  of  stating  difference^  "  The 
subject  is  the  same  "  implies,  and  may  be  meant  to  convey, 
the  truth  that  the  attributes  differ.  We  must  refer  to  the 
sequel  for  further  explanation,  but  at  present  our  concern  is 
briefly  to  point  out  that  an  identity  must  underlie  every 
judgment. 

But  how  is  this  possible  ?  "  A  is  prior  to  B,"  or  '*  to  the 
left  of  C,"  or  "equal  to  D."  The  judgment  asserts  the 
equality,  or  sequence,  or  position  of  two  subjects,  and  it 
surely  does  not  say  that  both  are  the  same.  We  must  try  to 
explain.  We  saw  that  all  judgment  is  the  attribution  of  an 
ideal  content  to  reality,  and  so  this  reality  is  the  subject  of 
which  the  content  is  predicated.  Thus  in  "  A  precedes  B," 
this  whole  relation  A  —  B  is  the  predicate,  and,  in  saying  this 
is  true,  we  treat  it  as  an  adjective  of  the  real  world.  It  is 
a  quality  of  something  beyond  mere  A  —  B.  But,  if  this  is  so, 
the  reality  to  which  the  adjective  A  — B  is  referred  is  the 
subject  of  A  — B,  and  is  the  identity  which  underlies  this 
synthesis  of  differences. 

It  is  identical,  not  because  it  is  simply  the  same,  but 
because  it  is  the  same  amid  diversity.  In  the  judgment, 
beside  the  mere  distinction  of  the  terms,  we  have  an  opposi- 
tion in  time  of  A  to  B.  And  the  subject  of  which  A  -  B  is 
asserted,  being  subject  to  these  differences,  is  thus  different 


30  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

in  itself,  while  remaining  the  same.  In  this  sense  every 
judgment  affirms  either  the  identity  which  persists  under 
difference,  or  the  diversity  which  is  true  of  one  single  subject. 
It  would  be  the  business  of  metaphysics  to  pursue  this 
discussion  into  further  subtleties.  We  should  there  have  to 
ask  if,  in  the  end,  every  possible  relation  does  not  involve  a 
something  in  which  it  exists,  as  well  as  somethings  between 
which  it  exists,  and  it  might  be  difficult  to  reconcile  the 
claims  of  these  prepositions.  But  we  have  already  reached 
the  limit  of  our  enquiries.  The  real  subject  which  is  implied 
in  judgment,  will  meet  us  again  in  the  following  Chapter  ;  and 
that,  we  hope,  may  make  clearer  some  points  which  at  present 
remain  obscure. 

III.  §  1 8.  We  have  given  some  preliminary  account  of 
judgment,  and  have  tried  to  dispose  of  some  erroneous  views. 
We  pass  now  to  our  third  task,  and  must  make  some  remarks 
on  the  developement  of  the  function.  As  we  have  defined  it 
above,  judgment  does  not  show  itself  at  all  the  stages  of 
psychical  evolution.  It  is  a  comparatively  late  acquisition  of 
the  miAd,  and  marks  a  period  in  its  upward  growth.  We 
should  probably  be  wrong  if  we  took  it  as  a  boundary  which 
divides  the  human  from  the  animal  intelligence  ;  and  in  any 
case  we  should  be  ill-advised  to  descend  here  into  the  arena 
of  theological  and  anti-theological  prejudice  (vid.  Book  III. 
Part  I.  Chap.  VI L).  It  is  better  to  treat  the  mind  as  a  single 
phenomenon,  progressing  through  stages,  and  to  avoid  all 
discussion  as  to  whether  the  lines,  by  which  we  mark  out  this 
progress,  fall  across  or  between  the  divisions  of  actual  classes 
of  animals.  Thus  with  judgment  we  are  sure  that,  at  a 
certain  stage,  it  does  not  exist,  and  that  at  a  later  stage  it  is 
found  in  operation  ;  and,  without  asking  where  the  transition 
takes  place,  we  may  content  ourselves  with  pointing  out  the 
contrast  of  these  stages.  The  digression,  if  it  be  such,  will 
throw  out  into  relief  the  account  we  have  already  given  of 
judgment.  For  judgment  is  impossible  where  truth  and 
falsehood,  with  their  difference,  are  not  known  ;  and  this 
difference  cannot  be  known  where  ideas  are  not  recognized 
and  where  nothing  exists  for  the  mind  but  fact. 


Chap.  I.]  THE   GENERAL   NATURE    OF   JUDGMENT.  3 1 

§  19.  I  do  not  mean  that  the  lower  forms,  or  that  any 
form,  of  soul-life  is  confined  to  the  apprehension  of  simple 
sensations.  If  the  soul  is  ever  the  passive  recipient  of  a 
given  product,  to  which  it  does  not  contribute  and  which  it 
does  not  idealize,  yet  in  all  actual  mind  a  further  step  is 
made,  and  we  always  possess  more  than  what  is  given 
through  sense.  The  impression,  so  to  speak,  is  supplemented 
and  modified  by  an  ideal  construction,  which  represents  the 
results  of  past  experience.  And  thus,  in  a  sense,  the  lowest 
animals  both  judge  and  reason,  and,  unless  they  did  so,  they 
must  cease  to  adjust  their  actions  to  the  environment.  But, 
in  the  strict  sense,  they  can  neither  reason  nor  judge ;  for 
they  do  not  distinguish  between  ideas  and  perceived  reality. 

That  the  thing  as  it  is,  and  as  it  appears  in  perception, 
are  not  the  same  thing,  is,  we  all  are  aware,  a  very  late  after- 
thought. But  it  is  equally  an  afterthought,  though  not 
equally  late,  that  there  is  any  kind  of  difference  between  ideas 
and  impressions.  For  a  more  primitive  mind  a  thing  is  or  it 
is  not,  is  a  fact  or  is  nothing.  That  a  fact  should  be,  and 
should  yet  be  an  appearance,  should  be  true  of,  and  belong 
to,  something  not  itself;  or  again  should  be  illusion,  should 
exist  and  yet  be  false,  because  its  content  is  an  adjective 
neither  of  itself  nor  of  any  other  substantive — these  distinc- 
tions are  impossible  for  an  early  intelligence.  A  nonentity  is 
not  anything  it  can  apprehend,  and  to  it  an  error  is  never  an 
illusion.  And  hence  for  this  mind  ideas  never  could  be 
symbols.     They  are  facts  because  they  are, 

§  20.  The  presentations  of  the  moment,  the  given  sensations, 
are  received  into  a  world  of  past  experience,  and  this  past 
experience  now  appears  in  the  form  of  ideal  suggestion.  In  the 
lowest  stages  of  mind  there  is  as  clear  a  difference  between 
the  datum  that  is  given  and  the  construction  that  is  made,  as 
there  can  be  in  the  highest.  But  it  is  one  thing  to  have  a 
difference  in  the  mind  and  another  to  perceive  it :  and  for  an 
early  intelligence  this  contrast  between  sensation  and  idea,  is 
quite  non-existent.  A  presentation  AB,  by  a  feeling  d,  produces 
an  action  Se,  or,  by  an  ideal  transition  b~d^  is  transformed  into 
ABD  ;  or  may  become  AC,  by  the  action  of  a-g,  if  g 
banishes  B,  and  c  is  supplied.     But,  in  all  these  cases,  and  in 


32  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

any  other  possible  case,  the  process  remains  entirely  latent. 
The  product  is  received  as  a  mere  given  fact,  on  a  level  with 
any  other  fact  of  sense. 

If  the  object,  as  first  perceived,  could  be  compared  with 
the  object  as  finally  constructed,  there  might  be  room  for  a 
doubt  if  the  fact  has  become,  or  has  been  made  by  the  mind. 
And  still  more  if  the  ideas  which  perception  excludes  were 
ever  attended  to  ;  if  rejected  suggestion,  conflicting  supplement, 
wrong  interpretation,  and  disappointed  action,  were  held 
before  the  mind,  then  a  reflection  might  take  place,  which 
would  antedate  the  slow  result  of  developement ;  and  the  sense 
of  illusion  would  awaken  the  contrast  of  idea  and  reality,  truth 
and  falsehood.  But  all  this  is  impossible.  For  the  leading 
feature  of  the  early  mind  is  its  entire  and  absolute  practicality. 
The  fact  occupies  the  soul  no  longer  and  no  further  than  it 
tends  to  produce  immediate  action.  The  past  and  the  future 
are  not  known  except  as  modifications  of  the  present.  There 
is  no  practical  interest  in  anything  but  the  given,  and  what 
does  not  interest  is  not  anything  at  all.  Hence  nothing  is 
retained  in  its  original  character.  The  object,  in  its  relation  to 
present  desire,  changes  ceaselessly  in  conformity  with  past 
adventures  of  failure  or  success.  It  contracts  or  extends  itself, 
as  the  case  may  be,  but  it  still  remains  the  mere  given  object. 
And  while  the  ideas  it  assimilates  become  part  of  presentation, 
the  ideas  it  excludes  are  simply  nothing  at  all. 

At  a  late  stage  of  mind,  among  intelligent  savages,  the 
doctrine  of  a  dream-world  brings  home  to  us  the  fact,  that  a 
mere  idea,  which  exists  and  is  unreal,  is  a  thought  not  easy  to 
lay  hold  of  thoroughly.  And,  if  we  descend  in  the  scale  no 
further  than  to  dogs,  we  are  struck  by  the  absence  of  theo- 
retical curiosity.  Let  them  see  an  appearance  to  be  not 
what  it  seemed,  and  it  instantly  becomes  a  mere  nonentity. 
An  idea,  we  may  say,  is  the  shadow  of  an  object ;  and  that  to 
a  savage  is  another  kind  of  object,  but  to  a  dog  it  is  the  thing 
or  just  nothing  at  all.  The  dog  has  not  entered  on  that 
process  of  reflection  which  perhaps  has  not  led  to  any  very 
sure  result.  When  his  heart,  like  ours,  is  baflled  and  oppressed, 
and  gives  matter  to  his  brain  it  has  no  strength  to  cope  with, 
he  can  neither  send  his  hopes  into  another  world  than  this,  nor 


Chap.  L]  THE   GENERAL   NATURE   OF  JUDGMENT.  33 

repeat  like  a  charm,  and  dream  that  he  believes,  that  appear- 
ances may  be  nothing  to  a  soul  which  feels  them.  I  do  not 
know  the  formula  which  would  prove  to  his  mind  a  satisfactory 
solution  of  his  practical  troubles  ;  but  his  system  of  logic,  if  he 
had  one,  would  be  simple  ;  for  it  would  begin,  I  am  sure,  and 
would  end  with  this  axiom,  "What  is  smells,  and  what  does 
not  smell  is  nothing." 

§  21.  It  would  be  difficult  to  detail  the  steps  of  the  process 
by  which  ideas,  as  such,  become  objects  of  knowledge,  and  with 
truth  and  falsehood  judgment  comes  in.  And,  apart  from 
this  difficulty,  there  is  a  question  of  fact  which  would  con- 
stantly arise.  Given  a  certain  stage  of  developement,  does 
judgment  already  exist  there  or  not }  It  might  perhaps  be 
right  to  connect  the  distinctions  of  truth  and  falsehood  in 
general  with  the  acquisition  of  language,  but  it  is  hard  to  say 
where  language  begins.  And,  in  the  stage  before  language, 
there  are  mental  phenomena  which  certainly  suggest  the 
effective  distinction  of  sensation  and  idea. 

The  provision  made  beforehand  for  changes  to  come  can 
not  always  be  taken  as  valid  evidence.  It  seems  clear  that, 
in  many  cases,  we  should  be  wrong  in  supposing  any  know- 
ledge of  the  future,  as  opposed  to  the  present.  It  is  certain 
at  least  that  a  presentation,  accompanied  by  or  transformed 
by  feelings,  is  as  effective  practically  as  the  clearest  idea.  But 
in  certain  animals  there  are  much  stronger  indications.  When 
artful  contrivances,  suitable  to  unseen  events,  are  used  in  the 
pursuit  of  prey,  we  are  led  to  conclude  that  the  difference  of 
the  situation,  as  it  actually  is  and  as  it  is  anticipated,  nmst 
come  before  the  mind.  And,  where  desire  is  unsatisfied,  it  is 
not  always  mere  feeling  as  against  the  object  which  pervades 
the  soul.  The  image  of  the  desired,  as  against  present  per- 
ception, floats  or  is  held  before  the  attention,  and  the  feeling 
of  pain,  we  may  suppose,  must  sharpen  the  contrast  until  at 
length  the  difference  is  seen.  And  we  can  mention  here 
what  perhaps  may  be  an  outward  symptom  of  the  change.  No 
one  can  have  been  much  with  domestic  animals,  and  failed  to 
observe  their  constant  and  increasing  use  of  the  imperative. 
They  seem  at  least  to  know  what  they  desire,  to  expect 
assistance,   and   to   be   surprised    at   non-compliance.      And 

D 


34  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

though  mere  urgency  of  feeling,  in  the  absence  of  ideas,  might 
account  for  their  tone,  this  interpretation  would  at  times  some- 
what strain  the  phenomena. 

But,  if  this  is  so,  then  judgment  must  come  before  language, 
and  certainly  cannot  be  distinctively  human.  And,  just  as 
after  language  has  been  developed,  we  do  often  dispense  with 
it ;  just  as  the  lowest,  and  perhaps  the  highest  of  our  thinking, 
goes  on  without  any  words  in  the  mind,  so  we  may  suppose, 
before  speech  was  developed,  the  differentia  of  judgment 
already  existed. 

We  are  not  concerned  in  the  controversy  to  which  this 
might  give  rise.  If  we  only  know  what  we  mean  by  judg- 
ment, it  is  little  to  our  purpose  where  first  it  appears,  and 
what  animal  first  reaches  it.  The  question  is  not  at  all  easy 
to  settle,  and  in  passing  I  will  merely  suggest  a  reflection.  It 
is  not  enough  to  show  that  in  the  mind  of  an  animal  an  image 
exists  together  with  a  presentation  of  sense,  and  that  this 
image,  partly  the  same  as  the  presented,  is  in  collision  with  it, 
and  again  leads  to  action  in  relation  to  the  presented.  All 
this  may  exist,  and  yet  the  differentia  still  be  absent ;  the 
image  may  not  be  seen  to  be  mere  appearance,  to  be  either 
not  real  at  all,  or  less  real  than  the  sensation.  For,  if  the 
image  is  taken  in  relation  to  the  perception,  they  may  both  be 
apprehended  as  one  continuous  changing  fact :  the  prey  may 
be  seen  as  pursued  and  captured,  and  the  actual  object  may 
appear  to  pass  into  the  desired.  And,  where  failure  makes 
this  impossible,  what  may  after  all  be  wanting  is  the  intel- 
lectual identification  of  the  image  with  the  object.  Apart 
from  this  logical  process,  we  have  a  mere  collision  in  the  mind 
of  two  realities,  whose  struggle  is  felt.  We  have  contest,  and 
perhaps  a  following  ejection  ;  but  we  have  no  subjection,  no 
degradation  of  one  fact  to  the  level  of  an  appearance,  that 
exists  but  in  our  heads.  And  in  this  case  judgment  would 
not  have  taken  place. 

§  22.  It  might  be  interesting  elsewhere  to  discuss  at  length 
these  puzzles  in  psychology,  but  it  will  repay  us  better  to  pass 
to  what  is  more  certain.  It  is,  in  the  first  place,  the  retetition 
of  the  false  idea  which  tends  to  provoke  comparison  with 
reality,  and  which  leads  the  way  to  the  knowledge  of  appear- 


Chap.  L]  THE  GENERAL   NATURE   OF  JUDGMENT.  35 

ance  and  truth  and  falsehood.  And,  in  the  second  place,  it  is 
language  which,  if  it  does  not  originate,  at  least  ensures  and 
sharpens  the  contrast.  When  gregarious  animals  utter  their 
ideas,  the  word  is  in  a  manner  more  permanent  than  the 
thought,  and  maintains  itself  against  the  fact  it  tries  to  ex- 
press.  ^And  the  spoken  thoughts  of  the  different  individuals 
are  sometimes  in  collision.  They  are  not  the  same  with  one 
another,  and  therefore  not  the  same  with  the  single  fact.  And 
speech  in  its  perversion  to  lies  and  deceit  makes  the  dullest  com- 
prehend that  words  and  ideas  can  be  and  be  real,  and  can  yet 
be  illusion  and  wholly  unreal  in  relation  to  facts.  At  this 
point  it  is  seen  that  the  word  and  the  thought  are  not  like 
other  things.  They  not  only  exist  but  also  mean  something, 
and  it  is  their  meaning  alone  which  is  false  or  true.  They  are 
seen  to  be  symbols,  and  this  insight  it  is  which  in  the  strict 
sense  constitutes  judgment. 

For  in  the  early  stage,  to  repeat  it  once  more,  the  image  is 
not  a  symbol  or  idea.  It  is  itself  a  fact,  or  else  the  facts 
eject  it  The  real,  as  it  appears  to  us  in  perception, 
connects  the  ideal  suggestion  with  itself,  or  simply  expels 
it  from  the  world  of  reality.  But  judgment  is  the  act  which, 
while  it  recognizes  the  idea  as  appearance,  nevertheless  goes 
on  to  predicate  it.  It  either  attributes  the  idea  to  reality,  and 
so  agirms  that  it  is  true,  or  pronounces  it  to  be  merely  a  bare 
idea,  and  that  the  facts  exclude  the  meaning  it  suggests. 
The  ideal  content  which  is  also  fact,  and  the  ideal  content 
which  is  nothing  beyond  itself,  are  truth  and  falsehood  as  they 
appear  in  judgment. 

§  23.  Our  object  in  the  foregoing  has  been,  not  to 
chronicle  a  psychological  transition,  but  to  mark  out  distinc- 
tive stages  and  functions.  We  must  endeavour,  in  con- 
clusion, to  obviate  a  very  fatal  mistake.  The  gulf  between 
the  stage  of  mind  that  judges  and  the  mind  that  has  not 
become  aware  of  truth,  may  seem  hard  to  bridge,  and  the 
account  we  have  given  may  seem  to  rend  facts  apart.  We 
may  be  thought  in  our  extremity,  when  with  natural  con- 
ditions no  progress  is  possible,  to  have  forced  upon  the  stage 
a  heaven-sent  faculty.  On  one  side  of  your  line,  we  may  be 
told,  you  possess  explicit  symbols  all  of  which  are  universal, 

D  2 


36  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

and  on  the  other  side  you  have  a  mind  which  consists  of  mere 
individual  impressions  and  images,  grouped  by  the  laws  of 
a  mechanical  attraction.  The  distinction  you  have  made 
amounts  to  a  divorce.  The  higher  stage  can  not  exist  as  you 
describe  it,  or  can  not  at  least  be  developed  from  the  lower. 

In  the  sequel  I  shall  criticize  the  whole  doctrine  of  the 
"  Association  of  ideas,"  but  at  present  I  will  say  thus  much  by 
anticipation.  I  agree  that,  if  the  lower  stages  of  the  mind 
were  really  what  they  are  in  most  English  psychologies,  it 
never  would  in  any  way  be  possible  to  pass  to  the  stage 
where  ideas  are  used  in  judgment.  And  this  consequence 
I  desire  to  accentuate  and  to  emphasize.  But  the  fashionable 
doctrine  of  "  association,"  in  which  particular  images  are  recalled 
by  and  unite  with  particular  images,  is,  I  think,  not  true  of  any 
stage  of  mind  (vid.  Book  II.  Part  II.  Chap.  I.).  It  does  not 
exist  outside  our  psychology.  From  the  very  first  beginnings 
of  soul-life  universals  are  used.  It  is  because  the  results  of 
experience  are  fixed  in  an  ideal  and  universal  form,  that 
animals  are  able,  I  do  not  say  to  progress,  but  to  maintain 
themselves  in  bare  existence. 

§  24.  In  England  I  am  afraid,  the  faithful  tradition  of 
accumulated  prejudice,  in  which  are  set  the  truths  of  the 
"  Philosophy  of  Experience,"  well-nigh  makes  idle  an  appeal 
to  the  fact.  But  I  will  try  to  state  the  fact,  however  idly.  It 
is  not  true  that  particular  images  are  ever  associated.  It  is 
not  true  that  among  lower  animals  universal  ideas  are  never 
used.  What  is  never  used  is  a  particular  idea,  and,  as  for 
association,  nothing  ever  is  associated  without  in  the  process 
being  shorn  of  particularity.  I  shall  hereafter  have  to  enlarge 
on  the  latter  statement,  and  at  present  will  deal  with  the  false 
assertion,  that  merely  individual  ideas  are  the  early  furniture 
of  the  primitive  mind. 

In  the  first  place  it  seems  patent  that  the  lower  animals 
have  not  any  idea  about  the  individual.  To  know  a  thing  as 
the  one  thing  in  the  world,  and  as  different  from  all  others,  is 
not  a  simple  achievement.  If  we  reflect  on  the  distinctions 
it  implies,  we  must  see  that  it  comes  late  to  the  mind.  And, 
on  turning  to  facts,  we  find  that  animals  of  superior  intel- 
ligence are  clearly  without  it,  or  give  us  at  least  no  reason 


Chap.  L]  THE   GENERAL   NATURE   OF  JUDGMENT.  3/ 

at  all  to  think  that  they  possess  it.  The  indefinite  universal, 
the  vague  felt  type,  which  results  from  past  perceptions  and 
modifies  present  ones,  is  palpably  the  process  of  their  in- 
tellectual experience.  And  when  young  children  call  all  men 
father,  it  is  the  merest  distortion  of  fact  to  suppose  that 
they  perceive  their  father  as  individual,  and  then,  perceiving 
other  individuals,  confuse  a  distinction  they  previously  have 
made. 

But  this  is  hardly  the  real  point  at  issue.  To  know  the 
individual  as  such  will  be  admitted  to  be  a  late  achievement. 
It  can  hardly  be  maintained  that  a  rude  intelligence,  when  it 
holds  a  type  and  rejects  what  disagrees  with  it,  can  be  awace^-Y 
of  that  type  as  an  unique  individual.  The  question  is  really 
as  to  the  2/j-^  madexif  images  in  early  knowledge.  ..Are  the^^  \ 
tised  as  universals,  or  used  as  particulars  ?  _  ,^J 

'  5  25.  it  is  agreed  on  both  sides  that,  as  psychical  exis- 
tences, ideas  are  particular  like  all  other  phenomena.  The 
controversy  is  confined  to  the  use  we  make  of  them.  I  should 
maintain  that,  so  far  as  they  remain  particular,  they  are  simple 
facts,  and  not  ideas  at  all ;  and  that,  where  they  are  employed 
to  extend  or  to  modify  experience,  they  are  never  used  in 
their  particular  form.  When  A-B  is  presented  in  perception, 
we  are  told  that  the  result  of  a  past  perception  B-C  appears 
as  particular  images  b-c,  and  that  these  images,  called  up, 
unite  with  the  presentation.  But  nothing  could  be  more  false. 
It  is  not  true  that  all  the  marks,  and  relations,  and  differences, 
which  constitute  the  particularity  of  b  and  c,  appear  in  the 
resultant  A-B-C,  or  were  in  any  way  used  in  order  to  produce 
it.  The  image  ^,  besides  its  content  as  ^,  had  the  indefinite 
detail  of  all  psychical  phenomena  ;  but  it  was  not  this  but 
the  universal  c  which  was  used  in  A-B-C,  and  it  is  the  per- 
ception A-B  that  re-particularizes  c  in  accordance  with  itself 
And,  if  this  is  so,  we  must  say  that  what  really  operates  is  a 
connection  between  universal  ideas.  We  have  already,  in  an 
unconscious  form,  what,  when  made  explicit,  is  the  meaning 
of  symbols. 

I  must  trust  to  the  sequel  for  elucidation  (vid.  Book  II.  II. 
Chap.  I.),  but  the  subject  is  so  important  that  I  will  venture  to 
insert  some  illustrations.    When  to-day  I  reach  the  place  where 


38  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

yesterday  my  dog  has  either  chased  a  cat  or  fought  with  an 
antagonist,  the  perception  as  we  say  "  calls  up  "  the  ideas,  and 
he  runs  eagerly  forward.  His  experience,  we  will  suppose, 
was  of  a  white  cat  or  a  black  retriever  with  a  large  brass 
collar.  To-day  images  are  "  called  up,"  not  so  definite  perhaps, 
but  still  certainly  with  some  detail,  and  we  will  suppose  that 
the  detail  reproduces  the  experience.  To-day  it  is  a  black 
cat  that  is  found  in  the  place,  but  with  an  ordinary  dog  that 
will  make  no  difference.  The  whiteness  of  the  image  is  quite 
irrelevant.  Or  again,  if  to-day  another  dog  be  perceived,  if 
only  that  dog  be  not  glaringly  different,  an  ordinary  dog  will 
certainly  attack  him,  and  the  less  intelligent  he  is  the  more 
catholic  is  his  action.  For  it  is  not  the  whole  image  but  a 
portion  of  the  content  which  operates  in  his  mind.  He  may 
turn  from  a  small  dog  or  a  white  dog  or  a  smooth-coated  dog, 
but  size,  blackness,  and  roughness,  are  the  typical  ideas  which 
will  certainly  operate.  It  may  be  said,  no  doubt,  that  the 
ideas  are  particular,  that  they  differ  from  the  perception,  and 
that  it  is  the  fault  of  the  animal  which  fails  to  distinguish 
them.  But  why,  I  reply,  does  it  fail  to  distinguish }  Is  a 
creature  intelligent  as  a  terrier  unable  to  see  the  difference 
between  a  white  and  black  cat,  or  a  Newfoundland  and  a 
sheep  dog .?  "  Yes,"  I  shall  be  told,  "  he  can  if  he  attends  to 
them,  but  here,  although  they  both  are  present,*  he  does  not 
attend  to  them."  But  if  so,  I  must  rejoin,  if  the  differences 
are  not  used,  but  remain  inoperative,  is  not  this  a  clear  proof 
that  what  operates,  and  what  is  used,  is  a  portion  of  the 
content,  which  is  permanent  amid  differences,  and  which  later 
becomes  the  universal  meaning. 

Again,  if  an  animal  has  been  burnt  one  day  at  the  kitchen 
fire,  the  next  day  it  may  shrink  from  a  lighted  match.     But 

*  This  is  a  false  assumption  as  will  be  shown  hereafter.  In  the  first 
place  it  is  not  true  that,  when  the  mind  goes  from  A  B  to  C,  it  has  to  pass 
through  a  particular  image  d.  In  the  next  place,  if  the  particular  d  be 
present,  we  have  no  reason  to  suppose  that  it  will  have  the  qualities  of 
the  original  perception  B.  If  a  white  cat  has  been  seen  to-day,  we  saw 
that  next  day,  if  its  image  is  white,  the  whiteness  of  that  image  need  not 
be  used  ;  and  again  if  its  whiteness  was  not  an  object  of  interest,  there  is 
no  reason  whatever  why  the  image  should  be  white,  and  not  of  some  other 
hue.     The  generalized  result  left  by  past  experience  is  always  mutilated. 


Chap.  L]  THE   GENERAL   NATURE   OF   JUDGMEN^^        39"^  ^  S|^ 

how  different  are  the  two.  How  much  more  unlike  than  like. 
Will  you  say  then  that  the  match  can  not  operate  unless  It 
first  summons  up,  and  then  is  confused  with  the  image  of  a 
kitchen  fire  ;  or  will  you  not  rather  say  that  a  connection 
between  elements,  which  are  none  of  them  particular,  is  pro- 
duced in  the  mind  by  the  first  experience  ?  But,  if  so,  from 
the  outset  universals  are  used,  and  the  difference  between  the 
fact  and  the  idea,  the  existence  and  the  meaning,  is  uncon- 
sciously active  in  the  undeveloped  intelligence. 

§  26.  We  must  anticipate  no  further.  In  another  place 
we  shall  show  the  fictitious  nature  of  the  "  Laws  of  Asso- 
ciation," as  they  have  been  handed  down  by  our  prevalent 
tradition.  Our  object  here  has  been,  in  passing,  to  show  that 
the  symbolic  use  of  ideas  in  judgment,  although  no  early 
process  of  the  mind,  is  a  natural  result  of  mental  develope- 
ment.  From  the  very  first  beginnings  of  intelligence  it  is 
the  type  that  operates  and  not  the  image.  The  instance  as 
such  is  never,  and  can  never  be,  retained  in  the  soul.  The 
connection  of  certain  elements  m  its  content  is  all  it  leaves 
behind.  You  may  calljt,  if  you  please,  mere  impotence  of  our 
imagination,  or  you  may  call  it  that  idealizing  function  of  the 
mind  which  is  the  essence  of  intelligence,  still  the  fact  remains 
that  never  at  any  stage  can  any  fact  be  retained  without  some 
mutilation,  some  removal  of  that  detail  which  makes  it  par- 
ticular. The  lower  we  descend  in  the  growth  of  our  own 
functions,  or  in  the  scale  of  animate  nature,  the  more  typical, 
the  less  individual,  the  less  distinct,  the  more  vaguely  uni- 
versal and  widely  symbolic  is  the  deposit  of  experience.  It 
is  not  symbolic  in  the  sense  that  the  meaning  is  at  first  per- 
ceived to  be  other  than  the  fact.  It  is  not  universal  in  the 
sense  that  analysis  has  distinguished  the  relevant  from  the 
irrelevant  detail,  and  found  elements  more  simple,  and  syn- 
theses wider  than  are  suggested  by  mere  sense.  But  in  the 
sense  of  not  using  the  particular  as  particular,  and  of  taking 
the  meaning  while  leaving  the  existence,  in  the  sense  of  in- 
variably transcending  the  given,  and  of  holding  true  always 
and  valid  everywhere  what  has  ever  and  anywhere  once  been 
experienced,  the  earliest  and  the  latest  intelligence  are  the 
same  from  one  end  to  the  other  of  the  scale  of  life. 


40  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 


CHAPTER   II. 

THE  CATEGORICAL  AND  HYPOTHETICAL  FORMS  OF 
JUDGMENT. 

§  I.  In  the  foregoing  chapter  we  have  attempted  roughly  to 
settle  the  main  characteristics  of  judgment.  The  present  chapter 
will  both  support  and  deepen  our  conclusion.  It  will  deal  with 
problems,  in  part  familiar  to  those  who  have  encountered  the 
well-known  discussion  aroused  by  Herbart.  The  length  and 
the  difficulty  of  this  second  chapter  may  perhaps  be  little 
warranted  by  success,  but  I  must  be  allowed  to  state  before- 
hand that  both  are  well  warranted  by  the  importance  of  the 
subject  in  modern  logic. 

A  judgment,  we  assume  naturally,  says  something  about 
some  fact  or  reality.  If  we  asserted  or  denied  about  anything 
else,  our  judgment  would  seem  to  be  a  frivolous  pretence. 
We  not  only  must  say  something,  but  it  must  also  be  about 
something  actual  that  we  say  it.  For  consider ;  a  judgment 
must  be  true  or  false,  and  its  truth  or  falsehood  cannot  lie  in 
itself  They  involve  a  reference  to  a  something  beyond. 
And  this,  about  which  or  of  which  we  judge,  if  it  is  not  fact, 
what  else  can  it  be } 

The  consciousness  of  objectivity  or  necessary  connection, 
in  which  the  essence  of  judgment  is  sometimes  taken  to  lie, 
will  be  found  in  the  end  to  derive  its  meaning  from  a  reference 
to  the  real.  A  truth  is  not  necessary  unless  in  some  way  it 
is  compelled  to  be  true  (vid.  Chap.  VII.).  And  compulsion  is 
not  possible  without  something  that  compels.  It  will  hence 
be  the  real,  which  exerts  this  force,  of  which  the  judgment  is 
asserted.  We  may  indeed  not  affirm  that  the  suggestion  S-P 
itself  is  categorically  true  of  the  fact,  and  tkat  is  not  our 
judgment.     The  actual  judgment  asserts  that  S-P  is  forced 


Chap.  II.]  FORMS  OF  JUDGMENT.  4 1 

On  our  minds  by  a  reality  x.  And  this  reality,  whatever  it 
may  be,  is  the  subject  of  the  judgment.  It  is  the  same  with 
objectivity.  If  the  connection  S-P  holds  outside  my  judg- 
ment, it  can  hardly  hold  nowhere  or  in  nothingness.  It  must 
surely  be  valid  in  relation  to  something,  and  that  something 
must  be  real.  No  doubt,  as  before,  S-P  may  not  be  true 
directly  of  this  fact ;  but  then  that  again  was  not  what  we 
asserted.  The  actual  judgment  affirms  that  S-P  is  in  con- 
nection with  X.  And  this  once  again  is  an  assertion  about 
fact. 

There  is  a  natural  presumption  that  truth,  to  be  true,  must 
be  true  of  reality.  And  this  result,  that  comes  as  soon  as  we 
reflect,  will  be  the  goal  we  shall  attain  in  this  chapter.  But 
we  shall  reach  it  with  a  struggle,  distressed  by  subtleties,  and 
perhaps  in  some  points  disillusioned  and  shaken. 

§  2.  Less  serious  difficulties  we  may  deal  with  at  once.  "  A 
four-cornered  circle  is  an  impossibility,"  we  are  told,  does  not 
assert  the  actual  existence  of  a  four-cornered  circle  (Herbart, 
I.  93).  But  the  objection  is  irrelevant,  unless  it  is  maintained 
that  in  every  case  we  affirm  the  reality  of  the  grammatical 
subject.*  And  this  clearly  is  not  always  what  we  mean  to  assert. 
And  such  further  examples  as  "  There  are  no  ghosts,"  or  "  This 
thought  is  an  illusion,"  may  be  likewise  disposed  of  It  is  not 
the  first  form  and  haphazard  conjunction  of  every  proposition 
which  represents  reality.  But,  in  every  proposition,  an  analysis 
of  the  meaning  will  find  a  reality  of  which  something  else  is 
affirmed  or  denied.  "  The  nature  of  space  excludes  the  con- 
nection of  square  and  round,"  "  The  world  is  no  place  where 
ghosts  exist,"  "  I  have  an  idea,  but  the  reality  it  refers  to  is 
other  than  its  meaning," — we  may  ofler  these  translations  as 
preliminary  answers  to  a  first  form  of  attack.  And  when 
Herbart  assails  us  with  "The  wrath  of  the  Homeric  gods 
is  fearful"  (I.  99),  we  need  give  no  ground  before  such  a 
weapon.  In  Homer  it  is  so ;  and  surely  a  poem,  surely  any 
imagination,  surely  dreams  and  delusions,  and  surely  much 
more  our  words  and  our  names  are  all  of  them  facts  of  a 
certain  kind.  )  Such  plain  distinctions  as  those  between 
existences  of  different  orders  should  never  have  been  confused, 
*  Ueberweg  seems  to  make  this  mistake,  Logik,  §  68. 


42  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

and  the  paradox  lies  on  the  side  of  those  who  urge  such  an 
objection.*     - 

And  if,  further,  the  discussion  take  the  misleading  form  of 
an  enquiry  into  the  copula,  we  find  merely  the  same  misunder- 
standings unknowingly  reproduced.  Wherever  we  predicate, 
we  predicate  about  something  which  exists  beyond  the  judg- 
ment, and  which  (of  whatever  kind  it  may  be)  is  real,  either 
inside  our  heads  or  outside  them.  And  in  this  way  we  must 
say  that  "is"  never  can  stand  for  anything  but  "exists.""|- 

§  3.  But  Herbart,  we  shall  find,  is  not  so  easily  disposed  of. 
He  was  not  the  man  first  uncritically  to  swallow  the  common- 
sense  doctrine  that  judgment  is  of  things,  and  then  to  stagger 
at  the  discovery  that  things  are  not  words,  or  fall  prostrate 
before  a  supposed  linguistic  revelation  of  the  nature  of  the 
copula.  In  denying  that  judgment  asserts  a  fact,  he  knew 
well  what  he  stood  on.  It  was  no  puzzle  about  the  gram- 
matical subject,  but  a  difficulty  as  to  the  whole  nature  of  truth 
and  of  ideas.  We  reflect  about  judgment,  and,  at  first  of 
course,  we  think  we  understand  it.  Our  conviction  is  that  it 
is  concerned  with  fact ;  but  we  also  see  that  it  is  concerned 
with  ideas.  And  the  matter  seems  at  this  stage  quite  simple. 
We  have  a  junction  or  synthesis  of  ideas  in  the  mind,  and  this 
junction  expresses  a  similar  junction  of  facts  outside.  Truth 
and- fact  are  thus  given  to  us  together,  the  same  thing,  so  to 
speak,  in  different  hemispheres  or  diverse  elements. 

*  I  admit  that  there  are  difficulties  which  for  the  moment  we  ignore. 
When  no  one  reads  Homer,  of  what  subject  can  we  predicate  the  wrath 
of  his  deities  ?  Though  the  meaning  of  a  term  is  a  fact,  most  certain 
and  quite  undeniable,  yet  where  is  that  fixed  connection  to  be  found  ? 
Does  it  lie  in  the  dictionaries  when  no  one  opens  them,  or  in  the  usage 
when  no  one  is  employing  the  word  ?  But  these  questions  bear  as  hardly 
on  fact  as  on  legend,  and  on  things  as  on  names.  Mathematical  truths 
at  the  least  hold  good  inside  mathematics.  But  where  are  mathe- 
matics ?  And  we  all  believe  that  arsenic  poisons,  but  if  at  the  moment 
no  dose  is  operating,  nor  any  one  in  the  world  is  thinking  of  arsenic, 
it  poisons  nothing.     We  shall  hereafter  return  to  the  discussion  of  this 

problem. 

t  The  reader  may  consult  Jordan.  Die  Zweideutigkeit  des  Coptila 
bei  Stuart  Mill,  Gymn.   Prog.  Stuttgart,   1870 ;  Brentano,  Psychologic, 

Buch  ii.    Cap.  7.      On  the  other  side  see    Drobisch.  Logik,  §§  55-6; 

Sigwart,  Logik,  I.  94. 


Chap.  IL]  FORMS  OF  JUDGMENT.  43 
But  a  further  reflection  tends  to  dissipate  our  confidence. 


I   Judgments,  we  find,  are  the  union  of  ideas,  and  truth  is  not 
I   found  except  in  judgments.     How  then  are  ideas  related  to 
Hrealities  ?     They  seemed  the  same,  but  they  clearly  are  not 
so,  and  their  difference    threatens  to  become  a  discrepancy. 
[  A  fact  is  individual,  an  idea  is  universal ;  a  fact  is  substantial, 
i  an  idea  is  adjectival ;  a  fact  is  self-existent,  an  idea  is  sym- 
bolical.    Is  it  not  then  manifest  that  ideas  are  not  joined  in 
the  way  in  which  facts  are }     Nay  the  essence  of  an  idea,  the 
more  it  is  considered,  is  seen  more  and  more  to  diverge  from 
reality.     And  we  are  confronted  by  the  conclusion  that,  so  far 
as  anything  is  true,  it  is  not  fact,  and,  so  far  as  it  is  fact,  it  can 
never  be  true.     Or  the  same  result  may  have  a  different  form. 
A  categorical  judgment  makes  a  real  assertion  in  which  some 
fact  is  affirmed  or  denied.     But,  since  no  judgment  can  do 
this,  they  all  in  the  end  are  hypothetical.     They  are  true  only 
of  and  upon  a  supposition.     In  asserting  S-P  I  do  not  mean 
that  S,  or  P,  or  their  synthesis,  is  real.     I  say  nothing  about 
any  union  in  fact.     The  truth  of  S-P  means  that,  if  I  stipjpose 
I  S,  I  am  bound  m  that  case  to  assert  S-P.     In  this  way  all 
judgments  are  hypothetical.* 

The  conclusion,  thus  urged  upon  us  by  Herbart,  follows,  I 
think,  irresistibly  from  the  premises.  But  the  premises  are 
not  valid.  Judgment,  we  saw  in  the  foregoing  chapter,  can 
not  consist  in  the  synthesis  of  ideas.  And  yet  it  will  repay 
us  to  pause  awhile,  and  to  enlarge  on  the  consequences  of  this 
erroneous  doctrine.  To  see  clearly  that,  if  judgment  is  the 
union  of  ideas,  there  then  can  be  no  categorical  judgment, 
is  a  very  great  step  in  the  understanding  of  Logic.  And, 
through  the  next  few  sections,  we  shall  endeavour  to  make 
this  conclusion  plain. 

§  4.  The  contrast  and  comparison  of  reality  and  truth  no 
doubt  involve  very  ultimate  principles.  To  enquire  what  is 
fact,  is  to  enter  at  once  on  a  journey  into  metaphysics,  the 
end  of  which  might  not  soon  be  attained.  For  our  present 
purpose  we  must  answer  the  question  from  a  level  not  much 
above  that  of  common  sense.     And  the  account  which  repre- 

*  Herbart,  Werke,  I.  92.  He  refers  here  to  Wolff,  by  whom,  in  this 
point  he  had  been  partially  anticipated.     Cf.  Fichte,  IVerke,  I.  69.  93. 


44  THE  PRINCIPLES  OF   LOGIC.  [Book  L 

sents  the  ordinary  view,  and  in  which  perhaps  we  may  most 
of  us  agree,  is  something  of  this  sort. 

The  real  is  that  which  is  known  in  presentation  or  intuitive 
knowledge.  It  is  what  we  encounter  in  feeling  or  perception. 
Again  it  is  that  which  appears  in  the  series  of  events  that 
occur  in  space  and  time.  It  is  that  once  more  which  resists 
our  wills  :  a  thing  is  real,  if  it  exercises  any  kind  of  force  or 
compulsion,  or  exhibits  necessity.j  It  is  briefly  what  acts  and 
maintains  itself  in  existence.  And  this  last  feature  seems 
connected  with  former  ones.  We  know  of  no  action,  unless  it 
shows  itself  by  altering  the  series  of  either  space  or  time,  or 
both  together;  and  again  perhaps  there  is  nothing  which 
appears  unless  it  acts.  But  the  simplest  account,  in  which  the 
others  possibly  are  all  summed  up,  is  given  in  the  words. 
The  real  is  self-existent.  And  we  may  put  this  otherwise  by 
saying,  The  real  is  what  is  individual. 

It  is  the  business  of  metaphysics  to  subject  these  ideas  to 
a  systematic  examination.  We  must  content  ourselves  here 
with  taking  them  on  trust,  and  will  pause  merely  to  point  out 
a  common  misunderstanding.  It  is  a  mistake  to  suppose 
that  "  The  real  is  individual "  means  either  that  the  real  is 
abstractly  simple,  or  is  merely  particular.  Internal  diversity 
does  not  exclude  individuality,  and  still  less  is  a  thing  made 
self-existent  by  standing  in  a  relation  of  exclusion  to  others. 
Metaphysics  can  prove  that,  in  this  sense,  the  particular  is 
furthest  removed  from  self-existence.  The  individual  is  so  far 
from  being  merely  particular  that,  in  contrast  with  its  own 
internal  diversity,  it  is  a  true  universal  (cf  Chap.  VI.).  Nor 
is  this  a  paradox.  We  are  accustomed  to  speak  of,  and 
believe  in,  realities  which  exist  in  more  than  one  moment  of 
time  or  portion  of  space.  Any  such  reality  would  be  an 
identity  which  appears 'and  remains  the  same  under  differ- 
ences ;  and  it  therefore  would  be  a  real  universal.* 

§  5.  Such,  we   may  say,  are    some   of  the  points  which 

*  The  following  reflection  may  interest  the  reader.  If  space  and 
time  are  continuous,  and  if  all  appearance  must  occupy  some  time  or 
space — and  it  is  not  hard  to  support  both  these  theses — we  can  at  once 
proceed  to  the  conclusion,  no  mere  particular  exists.  Every  phenomenon 
will  exist  in  more  times  or  spaces  than  one ;  and  against  that  diversity 
will  be  itself  an  universal. 


Chap.  IL]  FORMS   OF  JUDGMENT.  45 

constitute  reality.  And  truth  has  not  one  of  them.  It  exists, 
as  such,  in  the  world  of  ideas.  And  ideas,  we  have  seen,  are 
merely  symbols.  They  are  general  and  adjectival,  not  sub- 
stantive and  individual.  Their  essence  lies  within  their  mean- 
ing and  beyond  their  existence.  The  idea  is  the  fact  with  its 
existence  disregarded,  and  its  content  mutilated.  It  is  but  a 
portion  of  the  actual  content  cut  off  from  its  reality,  and  used 
with  a  reference  to  something  else.     No  idea  can  be  real. 

If  judgment  is  the  synthesis  of  two  ideas,  then  truth 
consists  in  the  junction  of  unreals.  When  I  say.  Gold  is 
yellow,  then  certainly  some  fact  is  present  to  my  mind.  But 
universal  gold  and  universal  yellowness  are  not  realities,  and, 
on  the  other  hand,  what  images  of  yellow  and  gold  I  actually 
possess,  though  as  psychical  facts  they  have  real  existence, 
are  unfortunately  not  the  facts  about  which  I  desired  to  say 
anything.  We  have  seen  (Chap.  I.)  that  I  do  not  mean,  This 
image  of  gold  is  in  my  mind  joined  psychically  with  this  other 
image  of  yellow.  I  mean  that,  quite  apart  from  my  mental 
facts,  gold  in  general  has  a  certain  kind  of  colour.  I  strip 
away  certain  parts  from  the  mental  facts,  and,  combining 
these  adjectival  remnants,  I  call  the  synthesis  truth. 

But  reality  is  not  a  connection  of  adjectives,  nor  can  it  so 
be  represented.  Its  essence  is  to  be  substantial  and  indivi- 
dual. But  can  we  reach  self-existence  and  individual  character 
by  manipulating  adjectives  and  putting  universals  together.? 
If  not,  the  fact  is  not  given  directly  in  any  truth  whatsoever. 
It  can  never  be  stated  categorically.  And  yet,  because  ad- 
jectives depend  upon  substantives,  the  substantive  is  implied. 
Truth  will  then  refer  to  fact  indirectly.  (The  adjectives  of 
truth  presuppose  a  reality,  and  in  this  sense  all  judgment  will 
rest  on  a  supposal.  It  is  all  hypothetical :  itself  will  confess 
that  what  directly  it  deals  with,  is  unreal.  ) 

§  6.  More  ordinary  considerations  might  perhaps  have  led 
us  to  anticipate  this  result.  The  common-sense  view  of  facts 
outside  us  passing  over  into  the  form  of  truth  within  us,  or 
copying  themselves  in  a  faithful  mirror,  is  shaken  and  per- 
plexed by  the  simplest  enquiries.  What  fact  is  asserted  in 
negative  judgments  t  Has  every  negation  I  choose  to  invent 
a  real  counterpart  in  the  world  of  things  }     Does  any  logical 


46  THE   PRINCIPLES  OF   LOGIC.  [Book  L 

negation,  as  such,  correspond  to  fact  ?  Consider  again  hypo- 
thetical judgments.  If  something  is,  then  something  else 
follows,  but  should  neither  exist,  would  the  statement  be 
false  }  It  seems  just  as  true  without  facts  as  with  them,  and, 
if  so,  what  fact  can  it  possibly  assert  .'*  The  disjunctive 
judgment  will  again  perplex  us.  "  A  is  ^  or  ^"  must  be  true 
or  false,  but  how  in  the  world  can  a  fact  exist  as  that  strange 
ambiguity  "^  or  cf'  We  shall  hardly  find  the  flesh  and 
blood  alternative  which  answers  to  our  "  or." 

If  we  think  these  puzzles  too  technical  or  sought  out,  let 
us  take  more  obvious  ones.  Have  the  past  and  the  future  we 
talk  of  so  freely  any  real  existence  .'*  Or  let  us  try  a  mere 
ordinary  categorical  affirmative  judgment,  "Animals  are 
mortal."  This  seems  at  first  to  keep  close  to  reality :  the 
junction  of  facts  seems  quite  the  same  as  the  junction  of  ideas. 
But  the  experience  we  have  gained  may  warn  us  that,  if  ideas 
are  adjectives,  this  can  not  be  the  case.  If  we  are  uncon- 
vinced, let  us  go  on  to  examine.  "Animals"  seems  perhaps 
to  answer  to  a  fact,  since  all  the  animals  who  exist  are  real. 
But  in  "Animals  are  mortal,"  is  it  only  the  animals  now 
existing  that  we  speak  of  t  Do  we  not  mean  to  say  that  the 
animal  born  hereafter  will  certainly  die  ?  The  complete  col- 
lection of  real  things  is  of  course  the  same  fact  as  the  real 
things  themselves,  but  a  difficulty  arises  as  to  future  indivi- 
duals. And,  apart  from  that,  we  scarcely  in  general  have  in 
our  m.inds  a  complete  collection.  We  7nean,  "  Whatever  is  an 
animal  will  die,"  but  that  is  the  same  as  If  anything  is  an 
animal  then  it  is  mortal.  The  assertion  really  is  about  mere 
hypothesis  ;  it  is  not  about  fact. 

In  universal  judgments  we  may  sometimes  understand 
that  the  synthesis  of  adjectives,  which  the  judgment  expresses,, 
is  really  found  in  actual  existence.  But  the  judgment  does 
not  say  this.  It  is  merely  a  private  supposition  of  our  own. 
It  arises  partly  from  the  nature  of  the  case,  and  partly  again 
from  our  bad  logical  tradition.  The  fact  that  most  adjectives 
we  conjoin  in  judgment  can  be  taken  as  the  adjectives  of 
existing  things,  leads  us  naturally  to  expect  that  this  will 
always  be  the  case.  And,  in  the  second  place,  a  constant 
ambiguity  arises  from  the  use  of  "  all  "  in  the  subject.     We 


CiiAP.  IL]  FORMS  OF  JUDGMENT.  47 

'  write  the  universal  in  the  form  "All  animals,"  and  then  take 
it  to  mean  each  actual  animal,  or  the  real  sum  of  existing 
animals.  But  this  would  be  no  more  an  universal  judgment 
than  "  A  B  and  C,  are  severally  mortal."  And  we  mean  nothing 
like  this.  In  saying  "All  animals,"  if  we  think  of  a  collection, 
we  never  for  a  moment  imagine  it  complete  ;  we  mean  also 
"  Whatever  besides  may  be  animal  must  be  mortal  too."  In 
universal  judgments  we  never  mean  "  all."  What  we  mean  is 
"any,"  and  "whatever,"  and  " whenever."  But  these  involve 
"  if." 

We  may  see  this  most  easily  by  a  simple  observation.  If 
actual  existence  were  really  asserted,  the  judgment  would  be 
false  if  the  existence  failed.  And  this  is  not  the  case.  It 
would  be  a  hazardous  assertion  that,  supposing  all  animal  life 
had  ceased,  mortality  would  at  once  be  -predicated  falsely, 
and,  with  the  re-appearance  of  animal  existence,  would  again 
become  true.  But  cases  exist  where  no  doubt  is  possible. 
"  All  persons  found  trespassing  on  this  ground  will  be  prose- 
cuted," is  too  often  a  prophecy,  as  well  as  a  promise.  But  it 
is  not  meant  to  foretell,  and,  though  no  one  trespasses,  the 

r statement  may  be  true.  "  All  triangles  have  their  angles 
equal  to  two  right  angles  "  would  hardly  be  false  if  there  were 
no  triangles.  And,  if  this  seems  strange,  take  the  case  of  a 
chiHagon.  Would  statements  about  chiliagons  cease  to  be 
true,  if  no  one  at  the  moment  were  thinking  of  a  chiliagon  } 
We  can  hardly  say  that,  and  yet  where  would  any  chiliagons 
exist }  There  surely  must  be  scientific  propositions,  which 
unite  ideas  not  demonstrable  at  the  moment  in  actual  ex- 
istence. But  can  we  maintain  that,  if  the  sciences  which 
produce  these  became  non-existent,  these  judgments  would 
have  ij>so  facto  become  false,  as  well  as  unreal } 

The  universal  judgment  is  thus  always  hypothetical.  It 
says  "  Given  one  thing  you  will  then  have  another,"  and  it 
says  no  more.     No  truth  can  state  fact. 

^'  §  7.  This  result  is  however  not  easy  to  put  up  with.  For, 
if  the  truth  is  such,  then  all  truths,  it  would  seem,  are  no 
better  than  false.  We  can  not  so  give  up  the  categorical 
judgment,  for,  if  that  is  lost,  then  everything  fails.  Let  us 
make  a  search  and  keep  to  this  question,  Is  there  nowhere  to 


48  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

be  found  a  categorical  judgment  ?  And  it  seems  we  can  find 
one.  ^^Universal  judgments  were  merely  hypothetical,  because 
they  stated,  not  individual  substantives,  but  connections  of 
adjectives.  But  in  singular  judgments  the  case  is  otherwise. 
Where  the  subject,  of  which  you  affirm  categorically,  is  one 
individual,  or  a  set  of  individuals,  your  truth  expresses  factj 
There  is  here  no  mere  adjective  and  no  hypothesis. 

These  judgments  are  divisible  into  three  great  classes. 
And  the  distinction  will  hereafter  be  of  great  importance,  (i) 
We  have  first  those  judgments  which  make  an  assertion  about 
that  which  I  now  perceive,  or  feel,  or  about  some  portion  of 
it.  "  I  have  a  toothache,"  "  There  is  a  wolf,"  "  That  bough  is 
broken."  In  these  we  simply  analyze  the  given,  and  may 
therefore  call  them  by  the  name  oi  Analytic  judgments  of  sense* 
Then  (ii)  we  have  Synthetic  judgments  of  sense,  which  state 
either  some  fact  of  time  or  space,  or  again  some  quality  of  the 
matter  given,  which  I  do  not  here  and  now  directly  perceive. 
"  This  road  leads  to  London,"  "  Yesterday  it  rained,"  "  To- 
morrow there  will  be  full  moon."  They  are  synthetic  because 
they  extend  the  given  through  an  ideal  construction,  and  they 
all,  as  we  shall  see,  involve  an  inference.  The  third  class  (iii), 
on  the  other  hand,  have  to  do  with  a  reality  which  is  never  a 
sensible  event  in  time.  "  God  is  a  spirit,"  "  The  soul  is  a  sub- 
stance." We  may  think  what  we  like  of  the  validity  of  these 
judgments,  and  may  or  may  not  decline  to  recognize  them  in 
metaphysics.     But  in  logic  they  certainly  must  have  a  place. 

§  8.  But,  if  judgment  is  the  union  of  two  ideas,  we  have 
not  so  escaped.  And  this  is  a  point  we  should  clearly  recog- 
nize. Ideas  are  universal,  and,  no  matter  what  it  is  that  we 
try  to  say  and  dimly  mean,  what  we  really  express  and 
succeed  in  asserting,  is  nothing  individual.  For  take  the 
analytic  judgment  of  sense.  The  fact  given  us  is  singular,  it 
is  quite  unique  ;  but  our  terms  are  all  general,  and  state  a 
truth  which  may  apply  as  well  to  many  other  cases.  In  "  I 
have  a  toothache "  both  the   I    and  the  toothache  are  mere 

*  These  analytic  and  synthetic  judgments  must  not  for  one  moment 
be  confounded  with  Kant's.  (  Every  possible  judgment,  we  shall  see 
hereafter,  is  both  analytic  and  synthetic.  Most,  if  not  all,  judgments 
of  sense  are  synthetic  in  the  sense  of  transcending  the  given. 


Chap.  II.]  FORMS   OF  JUDGMENT.  49 

generalities.  The  actual  toothache  is  not  any  other  toothache, 
and  the  actual  I  is  myself  as  having  this  very  toothache.  But 
the  truth  I  assert  has  been  and  will  be  true  of  all  other  tooth- 
aches of  my  altering  self  Nay  "  I  have  a  toothache,"  is  as 
true  of  another's  toothache  as  of  my  own,  and  may  be  met  by 
the  assertion,  "  Not  so  but  /  have  one."  It  is  in  vain  that  we 
add  to  the  original  assertion  "this,"  "here,"  and  "now,"  for 
they  are  all  universals.  They  are  symbols  whose  meaning 
extends  to  and  covers  innumerable  instances. 

Thus  the  judgment  will  be  true  of  any  case  whatsoever 
of  a  certain  sort ;  but,  if  so,  it  can  not  be  true  of  the  reality  ; 
for  that  is  unique,  and  is  a  fact  not  a  sort.  "That  bough  is 
broken,"  but  so  are  many  others,  and  we  do  not  say  which. 
"This  road  leads  to  London"  may  be  said  just  as  well  of  a 
hundred  other  roads.  "  To-morrow  it  will  be  full  moon,"  does 
not  tell  us  what  to-morrow.  Hereafter  it  will  constantly  be 
true  that,  on  the  day  after  this  day,  there  will  be  a  full  moon. 
And  so,  failing  in  all  cases  to  state  the  actual  fact,  we  state 
something  else  instead.  What  is  true  of  all  does  not  express 
this  one.  The  assertion  sticks  for  ever  in  the  adjectives  ;  it 
does  not  reach  the  substantive.  And  adjectives  unsupported 
float  in  the  air :  their  junction  with  reality  is  supposed  and 
not  asserted.  So  long  as  judgments  are  confined  to  ideas, 
their  reference  to  fact  is  a  mere  implication.  It  is  pre- 
supposed outside  the  assertion,  which  is  not  strictly  true  until 
we  qualify  it  by  a  suppressed  condition.  As  it  stands,  it  both 
fails  as  a  singular  proposition,  and  is  false  if  you  take  it  as  a 
strict  universal  {cf.  §  62  foil.). 

§  9.  But  judgment,  as  we  saw  in  the  foregoing  Chapter,  is 
not  confined  to  ideas,  and  can  not  by  any  means  consist  in 
their  synthesis.  (The  necessity  for  two  ideas  is  a  mere  delusion, 
and,  if  before  we  judged  we  had  had  to  wait  for  them,  we 
certainly  should  never  have  judged  at  all.  And  the  necessity 
for  the  copula  is  a  sheer  superstition.  Judgments  can  exist 
without  any  copula  and  with  but  one  idea.    ^ 

In  the  simplest  judgment  an  idea  is  referred  to  what  is 
given  in  perception,  and  it  is  identified  therewith  as  one  of  its 
adjectives.  There  is  no  need  for  an  idea  to  appear  as  the 
subject,  and,  even  when  it  so  appears,  we  must  distinguish  the 

E 


50  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

fact  from  grammatical  show.  It  is  present  reality  which  is 
the  actual  subject,  and  the  genuine  substantive  of  the  ideal 
content.  We  shall  see  hereafter  that,  when  "this"  "here'' 
and  "now"  seem  to  stand  as  subjects,  the  actual  fact  which 
appears  in  perception  is  the  real  subject,  to  which  these 
phrases  serve  to  direct  our  attention.  But  of  this  in  the 
sequel ;  we  have  seen  already,  and  have  further  to  see,  that 
all  judgments  predicate  their  ideal  content  as  an  attribute  of 
the  real  which  appears  in  presentation. 

It  is  from  this  point  of  view  that  we  must  resume  the 
discussion.  Standing  on  this  basis,  we  must  examine  afresh 
the  various  judgments  which  have  passed  "before  us,  and  must 
ask  for  their  meaning  and  further  validity.  Some  difficulties 
in  our  search  for  categorical  judgments  may  have  already 
disappeared ;  but  others  as  formidable  must  perhaps  be 
awaited.  And,  if  we  come  to  the  result  that  all  truth  in  the 
end  is  true  of  reality,  we  must  not  expect  to  maintain  that 
doctrine  in  its  crude  acceptation. 

§  10.  Our  first  movement  however  must  be  towards  a 
definition.  A  phrase  we  have  used  was  designedly  am- 
biguous. Are  we  to  hold  that  the  real,  which  is  the  ultimate 
subject,  ^and  which,  as  we  said,  appears  in  perception,  is 
identical  with  the  merely  momentary  appearance  }  We  shall 
see  that  this  can  not  be,  and  that  such  a  view  could  not 
possibly  account  for  the  facts.  At  present  we  may  offer 
a  preliminary  argument  against  this  mistake. 

The  subject  which  appears  in  the  series  of  time,  and  to 
which  we  attribute  our  ideas  as  predicates,  rriust  itself  be  real. 
And,  if  real,  it  must  not  be  purely  adjectival.  On  the 
contrary  it  must  be  self-existent  and  individual.  But  the 
particular  phenomenon,  the  momentary  appearance,  is  not 
individual,  and  is  so  not  the  subject  which  we  use  in 
judgment. 

§  II.  We  naturally  think  that  the  real,  at  least  as  we 
know  it,  must  be  present.  Unless  I  come  into  contact  with  it 
directly,  I  can  never  be  sure  of  it.  Nothing  in  the  end  but 
what  I  feel  can  be  real,  and  I  can  not  feel  anything  unless  it 
touches  me.      But  nothing  again  can  immediately  encounter 


p 

Chap.  II.]  FORMS   OF  JUDGMENT.  ^l 

me  save  that  which  is  present.  If  I  have  it  not  here  and  now, 
I  do  not  have  it  at  all. 

"  The  present  is  real  ; "  this  seems  indubitable.  And  are 
we  to  say  that  the  momentary  appearance  is  therefore  real } 
This  indeed  would  be  mistaken.  If  we  take  the  real  as  that 
which  is  confined  to  a  single  "  here  "  or  a  single  "  now  "  (in  this 
sense  making  it  particular),  we  shall  have  questions  on  our 
hands  we  shall  fail  to  dispose  of.  For,  beside  the  difficulties 
as  to  the  truth  of  all  universal  judgments,  we  are  threatened 
with  the  loss  of  every  proposition  which  extends  beyond  the 
single  instant.  Synthetic  judgments  must  at  once  be  banished 
if  the  real  is  only  the  phenomenon  of  a  moment.  Nothing 
either  past  or  future  in  time,  nor  any  space  I  do  not  directly 
perceive,  can  be  predicated  as  adjectives  of  our  one  "now" 
and  "here."  All  such  judgments  would  be  false,  for  they 
would  attribute  to  the  existent  qualities  which  confessedly  are 
non-existent,  or  would  place  the  real  as  one  member  in  a 
series  of  utter  unrealities. 

But  perhaps  we  feel  we  may  escape  this  consequence  ;  or  at 
all  events  feel  so  sure  of  our  premise  that  we  can  not  give  it 
up.  "  The  real  is  confined  to  one  here  or  one  now."  But 
supposing  this  true,  are  we  sure  we  know  what  it  is  we  under- 
stand by  our  "  now  "  and  "  here  "  t  For  time  and  extension 
seem  continuous  elements  :  the  here  is  one  space  with  the 
other  heres  round  it ;  and  the  now  flows  ceaselessly  and 
passes  for  ever  from  the  present  to  the  past. 

We  may  avoid  this  difficulty,  we  may  isolate  the  time  we 
call  the  present,  and  fix  our  now  as  the  moment  which  is,  and 
has  neither  past,  nor  future,  nor  transition  in  itself.  But  here 
we  fall  into  a  hopeless  dilemma.  This  moment  which  we 
take  either  has  no  duration,  and  in  that  case  it  turns  out  no 
time  at  all :  or,  if  it  has  duration,  it  is  a  part  of  time,  and  is 
found  to  have  transition  in  itself 

If  the  now  in  which  the  real  appears  is  purely  discrete, 
then  first  we  may  say  that,  as  characterized  by  exclusion,  the 
phenomenon,  if  apparent,  is  not  self-subsistent,  and  so  not  real. 
But  apart  from  that  objection,  and  to  return  to  our  dilemma, 
the  now  and  the  here  must  have  some  extension.  For  no  part 
of  space  or  time  is  a  final  element.     We  find  that  every  here 

E  2 


52  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

is  made  up  of  heres,  and  every  now  is  resolvable  into  nows. 
And  thus  the  appearance  of  an  atomic  now  could  not  show 
itself  as  any  one  part  of  time.  But,  if  so,  it  could  never  show 
itself  at  all.  Or,  on  the  other  hand,  if  we  say  the  appearance 
has  duration,  then,  like  all  real  time,  it  has  succession  in  itself, 
and  it  would  not  be  the  appearance  of  our  single  now.* 
From  all  which  it  is  clear  that  a  momentary  appearance 
will  not  give  us  the  subject  of  which  we  are  in  search. 

§  12.  It  is  a  mistake  to  suppose  that  the  present  is  a  part 
of  time,  indivisible  and  stationary,  and  that  here  and  now  can 
be  solid  and  atomic.  In  one  sense  of  the  word  the  present  is 
no  time.  Itself  no  part  of  the  process,  it  is  a  point  we  take 
within  the  flow  of  change.  It  is  the  line  that  we  draw  across 
the  stream,  to  fix  in  our  minds  the  relations  of  one  successive 
event  to  another  event.  "Now,"  in  this  sense,  stands  for 
"  simultaneous  with : "  it  signifies  not  existence  but  bare  position 
in  the  series  of  time.  The  reality  is  not  present  in  the  sense 
of  given  in  one  atomic  moment. 

What  we  mean,  when  we  identify  presence  with  reality,  is 
something  different.  The  real  is  that  with  which  I  come  into 
immediate  contact,  and  the  content  of  any  part  of  time,  any 
section  of  the  continuous  flow  of  change,  is  present  to  me  if  I 
directly  encounter  it.  What  is  given  in  a  perception,  though 
it  change  in  my  hands,  is  now  and  here  if  only  I  perceive  it. 
And  within  that  perception  any  aspect  or  part,  which  I 
specially  attend  to,  is  specially  present,  is  now  and  here  in 
another  sense  than  the  rest  of  that  content.  The  present  is 
the  filling  of  that  duration  in  which  the  reality  appears  to  me 

*  It  is  the  business  of  metaphysics  to  prove  these  points  at  length. 
If  time  consists  of  discrete  parts,  it  is  hard  to  see  how  the  fact  of  succes- 
sion can  possibly  be  explained,  unless  time  be  taken  between  these  parts 
of  time.  And  that  would  lead  to  untenable  conclusions.  But  it  is  the 
fact  of  change  which  shows  that  time  is  continuous.  The  rate  of  change, 
the  number  of  events  in  every  part  of  time,  may,  so  far  as  we  know,  be 
increased  indefinitely  :  and  this  means  that  in  every  part  of  time  more 
than  one  event  may  take  place.  If  the  parts  be  discrete,  then  not  only 
will  motion  imply  that  a  thing  is  in  several  places  in  one  time  (and  this 
is  a  fact),  but  also  (which  is  absurd)  that  throughout  all  these  places 
no  time  elapses,  that  they  are  strictly  contemporaneous.  I  should  be 
glad  to  enter  into  the  discussion  at  length,  but  the  subject  cannot  properly- 
be  treated  by  logic. 


Chap.  II.]  FORMS   OF  JUDGMENT.  53 

directly  :  and  there  can  be  no  part  of  the  succession  of  events 
so  small  or  so  great,  that  conceivably  it  might  not  appear  as 
present. 

In  passing  we  may  repeat  and  may  trace  the  connection 
of  those  shades  of  meaning  we  have  found  in  "  presence."  (i) 
Two  events  in  time  are  now  to  one  another,  if  both  are  given 
simultaneously  in  my  series,  (ii)  Since  the  real  appears  in  the 
series  of  time,  the  effort  to  find  it  both  present  and  existing 
within  that  series,  creates  the  fiction  of  the  atomic  now.  (iii) 
If  the  real  can  never  exist  in  time,  but  only  appear  there,  then 
that  part  of  the  series  in  which  it  touches  me  is  my  present, 
(iv)  And  this  suggests  the  reflection  that  presence  is  really 
the  negation  of  time,  and  never  can  properly  be  given  in  the 
series.  It  is  not  the  time  that  can  ever  be  present,  but  only 
the  content. 

§  13.  But  we  must  leave  these  intricacies.  We  must  be 
satisfied  with  knowing  that  the  real,  which  (we  say)  appears 
in  perception,  does  not  appear  in  one  single  moment.  And 
if  we  will  pause  and  reflect  for  a  little,  we  shall  see  how 
hardened  we  are  in  superstitions.  When  we  ask  for  reality, 
we  at  once  encounter  it  in  space  and  time.  We  find  opposed 
to  us  a  continuous  element  of  perpetual  change.  We  begin  to 
observe  and  to  make  distinctions,  and  this  element  becomes 
a  series  of  events.  And  here  we  are  tempted  to  deceive  our- 
selves grossly.  We  allow  ourselves  to  talk  as  if  there  existed 
an  actual  chain  of  real  events,  and  as  if  this  chain  were  some- 
how moved  past  us,  or  we  moved  along  it,  and  as  if,  whenever 
we  came  to  a  link,  the  machinery  stopped  and  we  welcomed 
each  new  link  with  our  "  here  "  and  our  "  now."  Still  we  do  not 
believe  that  the  rest  of  the  links,  which  are  not  here  and  now, 
do  all  equally  exist,  and,  if  so,  we  can  hardly  be  quite  sure  of 
our  chain.  And  the  link,  if  we  must  call  it  so,  which  is  now 
and  here,  is  no  solid  substance.  If  we  would  but  obsei-ve  it, 
we  should  see  it  itself  to  be  a  fluid  sequence  whose  parts  offer 
no  resistance  to  division,  and  which  is  both  now,  and  itself 
without  end  made  up  of  nows. 

Or  we  seem  to  think  that  we  sit  in  a  boat,  and  are  carried 
^own  the  stream  of  time,  and  that  on  the  bank  there  is  a  row 
.of  houses  with  numbers  on  the  doors.     And  we  get  out  of  the 


54  THE   PRINCIPLES  OF  LOGIC.  [Book  L 

boat,  and  knock  at  the  door  of  number  19,  and,  re-entering  the 
boat,  then  suddenly  find  ourselves  opposite  20,  and  having 
there  done  the  same,  we  go  on  to  21.  And,  all  this  while,  the 
firm  fixed  row  of  the  past  and  future  stretches  in  a  block 
behind  us  and  before  us. 

If  it  really  is  necessary  to  have  some  image,  perhaps  the 
following  may  save  us  from  worse.  Let  us  fancy  ourselves  in 
total  darkness  hung  over  a  stream  and  looking  down  on  it. 
The  stream  has  no  banks,  and  its  current  is  covered  and  filled 
continuously  with  floating  things.  Right  under  our  faces  is  a 
bright  illuminated  spot  on  the  water,  which  ceaselessly  widens 
.  and  narrows  its  area,  and  shows  us  what  passes  away  on  the 
ft  current.  And  this  spot  that  is  light  is  our  now,  our  present. 
We  may  go  still  further  and  anticipate  a  little.  We  have 
not  only  an  illuminated  place,  and  the  rest  of  the  stream  in 
total  darkness.  There  is  a  paler  light  which,  both  up  and 
down  stream,  is  shed  on  what  comes  before  and  after  our  now. 
And  this  paler  light  is  the  offspring  of  the  present.  Behind 
our  heads  there  is  something  perhaps  which  reflects  the  rays 
from  the  lit-up  now,  and  throws  them  more  dimly  upon  past 
and  future.  Outside  this  reflection  is  utter  darkness  ;  within  it 
is  gradual  increase  of  brightness,  until  we  reach  the  illumina- 
tion immediately  below  us. 

In  this  image  we  shall  mark  two  things,  if  we  are  wise.  It 
is  possible,  in  the  first  place,  that  the  light  of  the  present  may 
come  from  behind  us,  and  what  reflects  the  light  may  also 
bestow  it.  We  can  not  tell  that,  but  what  we  know  is,  that 
our  now  is  the  source  of  the  light  that  falls  on  the  past  and 
future.  Through  it  alone  do  we  know  there  exists  a  stream 
of  floating  things,  and  without  its  reflection  past  and  future 
would  vanish.  And  there  is  another  point  we  must  not  lose  sight 
of  There  is  a  difference  between  the  brightness  of  the  now, 
and  the  paler  revelation  of  past  and  future.  But,  despite  this 
difference,  we  see  the  stream  and  what  floats  in  it  as  one. 
We  overcome  the  difference.  And  we  do  so  by  seeing  the 
continuity  of  the  element  in  past  present  and  future.  It  is 
because,  through  the  different  illuminations,  there  are  points 
of  connection  offered  by  what  floats,  in  other  words,  a  same- 
ness of  content,  that  the  stream  and  its.  freightage  becomes  all 


Chap.  IL]  FORMS  OF  JUDGMENT.  55 

one  thing  to  us,  and  we  even  forget  that  most  of  what  we  see 
is  not  self-subsistent  but  borrowed  and  adjectival.  We  shall 
perceive  hereafter  that  time  and  space  beyond  here  and  now 
are  not  strictly  existent  in  the  sense  in  which  the  present  is. 
They  are  not  given  directly  but  are  inferred  from  the  present. 
And  they  are  so  inferred  because  the  now  and  here,  on  which 
the  light  falls,  are  the  appearance  of  a  reality  which  for  ever 
transcends  them,  and,  resting  upon  which,  we  go  beyond 
them. 

§  14.  But  this  is.  to  anticipate.  The  result,  which  at  present 
we  have  wished  to  make  clear,  is  that  the  now  and  here,  in 
which  the  real  appears,  are  not  confined  within  simply  discrete 
and  resting  moments.  They  are  any  portion  of  that  con- 
tinuous content  with  which  we  come  into  direct  relation. 
Examination  shows  that  not  only  at  their  edges  they  dissolve 
themselves  over  into  there  and  then,  but  that,  even  within 
their  limits  as  first  given,  they  know  no  repose.  Within  the 
here  is  both  here  and  there  ;  and  in  the  ceaseless  process  of 
change  in  time  you  may  narrow  your  scrutiny  to  the  smallest 
focus,  but  you  will  find  no  rest.  The  appearance  is  always  a 
process  of  disappearing,  and  the  duration  of  the  process  which 
we  call  our  present  has  no  fixed  length. 

It  will  be  seen  hereafter  that  in  the  above  reflections  we 
have  not  been  wandering.  Nor  will  it  be  long  before  we 
return  to  them,  but  we  must  now  rediscuss  from  a  better 
point  of  view  those  forms  of  judgment  we  before  laid 
down  (§  7). 

y  ^  ^S-  Judgment  is  not  the  synthesis  of  ideas,  but  the  refer- 
.  ence  of  ideal  content  to  reality.  From  this  basis  we  must 
now  endeavour  to  interpret  the  various  kinds  of  judgment  we 
have  met  with.  And,  beginning  with  the  singular  judgments 
of  §  7,  let  us  take  the  first  division  of  these,  which  were  called 
Analy^tic  judgments  of  sense. 

]  ^.  The  essence  of  these  is  to  hold  only  of  the  now,  and  not 
to  transcend  the  given  presentation.  They  may  have  neither 
grammatical  subject  nor  copula,  or  again,  on  the  other  hand, 
may  possess  one  or  both. 

A.  In  the  judgments  that  have  neither  copula  nor  subject, 


L 


56  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

an  idea  is  referred  {a)  to  the  whole  sensible  reality,  or  {^)  to 
some  one  part  of  it. 

(a)  When  we  hear  the  cry  of  "  Wolf,"  or  "  Fire,"  or  "  Rain," 
it  is  impossible  to  say  that  we  hear  no  assertion.  He  who 
raises  the  cry  is  always  taken  to  affirm,  to  have  uttered  a  sign 
and  to  have  used  it  of  the  real.  The  practical  man  would 
laugh  at  your  distinction  that,  in  exclaiming  "  Wolf,"  I  can 
not  be  a  liar,  because  I  use  no  subject  or  copula,  but  that,  if 
I  go  so  far  as  "  This  is  a  wolf,"  I  am  thereby  committed.  Such 
a  plea,  we  must  allow,  would  be  instantly  dismissed.  In  the 
"Wolf"  or  "Rain"  the  subject  is  the  unspecified  present  en- 
vironment, and  that  is  qualified  by  the  attribution  of  the  ideal 
content  "  Wolf"  or  "  Rain."  It  is  the  external  present  that  is 
here  the  subject.  But  in  some  moment  of  both  outward 
squalor  and  inward  wretchedness,  where  we  turn  to  one 
another  with  the  one  word  "  miserable,"  the  subject  is  here  the 
whole  given  reality. 

■  Such  single  words,  it  may  perhaps  be  said,  are  really 
interjections  and  never  predicates.  If  they  were  really 
interjections,  we  must  stubbornly  maintain,  they  could  not 
be  the  vehicle  of  truth  and  falsehood.  And  a  real  inter- 
jection that  is  nothing  besides,  is  not  so  common  as  some 
persons  suppose.  An  habitual  interjection  soon  gets  a 
meaning,  and  becomes  the  sign  of  a  received  idea,  which,  in 
reference  to  the  content,  may  be  an  assertion  of  truth  or 
falsehood. 

But  the  fact  is  really  beyond  all  question.  You  may  utter 
a  word  which  conveys  to  you,  and  which  you  know  conveys 
to  others  also,  a  statement  about  fact.  Unless  then  you 
are  deceiving,  you  must  be  judging.  And  you  certainly 
are  judging  without  any  other  subject  than  the  whole  sensible 
present. 

ifi)  But  this  is  an  extreme  case :  in  nearly  all  instances 
but  one  piece  of  the  present  is  the  real  subject.  We  qualify 
by  our  idea  some  one  given  aspect.  But  no  subject  or  copula 
appears  even  here.  A  common  understanding,  or  the  pointing 
of  a  finger,  is  all  that  serves  to  limit  the  reference.  Of  a 
visible  wolf  I  may  predicate  the  words  "  asleep  "  or  "  running," 
or  in  watching  a  sunset,  it  is  enough  for  me  to  say  the  word 


Chap.  II.]  FORMS  OF  JUDGMENT.  57 

"  down  "  or  "  gone,"  and  every  one  knows  I  am  judging  and 
affirming.  It  might  be  said,  no  doubt,  that  the  subject  is 
elided,  but  this  would  be  a  mere  linguistic  prejudice.  The 
genuine  subject  is  not  an  idea,  elided  or  expressed,  but  it  is 
the  immediate  sensible  presentation.* 

And  again  it  might  be  said  that  what  we  call  the  predicate 
is  really  the  subject  of  an  unexpressed  existential  judgment. 
But  this  cardinal  mistake  will  be  soon  disposed  of,  when 
hereafter  we  deal  with  that  class  of  judgments  (§  42). 

§  15.  B.  We  pass  next  to  those  analytic  judgments  where 
a  subject  is  expressed.  The  ideal  content  of  the  predicate  is 
here  referred  to  another  idea,  which  stands  as  a  subject.  But 
in  this  case,  as  above,  the  ultimate  subject  is  no  idea,  but  is 
the  real  in  presentation.  It  is  this  to  which  the  content  of 
both  ideas,  with  their  relation,  is  attributed.  The  synthesis  of 
the  ideal  elements  is  predicated  either  (a)  of  the  whole,  or  {(3) 
of  a  part,  of  that  which  appears. 

(a)  In  such  judgments  as  "  Now  is  the  time,"  "  It's  all  so 
dreary,"  or  "  The  present  is  dark,"  an  idea  takes  the  place  of 
the  unspoken  reference  of  the  preceding  section.  But  the 
subject  remains  in  both  cases  the  same.  An  idea,  it  is  true, 
intervenes  beween  the  reality  and  the  predicate,  and  holds  the 
place  of  immediate  subject.  But  a  moment's  consideration 
will  assure  us  that  the  subject  of  our  assertion  is  still  the 
presented.  The  immediate  subject  is  the  sign  of  a  reference, 
either  simple  or  embodying  implications,  to  the  whole  given 
reality. 

(/3)  We  have  a  further  advance  when  the  presented  fact  is 
not  the  whole  sensible  environment,  but  only  a  part  of  it. 
In  "  There  is  a  wolf,"  "  This  is  a  bird,"  or  "  Here  is  a  fire," 
"there"  "this  "  and  "here"  are  certainly  ideas,  and  stand  no 
doubt  for  the  subject  of  the  judgment:!  but,  the  moment  we 
examine  them,  we  find  once  more  a  reference  to  the  reality, 
not  now  indefinite  and  embracing  the  whole,  but  still  no  more 

*  For  a  further  explanation,  vid.  Chap.  III.  §  2. 

t  It  sounds,  perhaps,  rather  shocking  to  call  "there"  or  "here" 
subjects,  but,  if  the  text  is  understood,  I  need  make  no  defence.  On  the 
nature  of  the  ideas  of  "  this,"  "  now,"  and  "  here,"  we  shall  find  later  on 
a  good  deal  to  say. 


58  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

than  a  sign  of  distinction  and  indication.  If  these  ideas  are 
the  true  subject  of  a  judgment,  then  so  is  a  silent  pointing  with 
the  finger. 

j  §  16.  There  is  really  no  change  when  we  go  a  step  further, 
and  take  such  judgments  as  "  This  bird  is  yellow,"  "  That  stone 
is  falling,"  "  This  leaf  is  dead,"  The  idea,  which  stands  as  the 
grammatical  subject,  is  certainly  more  than  an  indefinite  refe- 
rence, more  even  than  a  sign  of  indication.  It  not  only  distin- 
guishes a  part  from  the  environment,  but  it  also  characterizes 
and  qualifies  it.  But  if,  before,  the  subject  we  meant  was  not 
an  idea,  but  was  presented  fact,  so  also  now  does  this  remain  the 
truth.  It  is  not  the  bare  idea,  symbolized  by  "  this  bird,"  of 
which  we  go  on  to  affirm  the  predicate.  It  is  the  fact  dis- 
tinguished and  qualified  by  "this  bird,"  to  which  the  adjective 
"yellow"  is  really  attributed.  The  genuine  subject  is  the 
thing  as  perceived,  the  content  of  which  our  analysis  has 
divided  into  "  this  bird  "  and  "  yellow,"  and  of  which  we  predi- 
cate indirectly  those  ideal  elements  in  their  union. 

The  same  account  holds  throughout  all  the  variety  of  these 
analytic  judgments.  Let  us  complicate  our  assertion.  "  The 
cow,  which  is  now  being  milked  by  the  milk-maid,  is  standing 
to  the  right  of  the  hawthorn  tree  yonder."  In  this  judgment 
we  have  not  one  thing  but  several,  and  more  than  one  state- 
ment about  their  relations.  But  it  is  still  a  part  of  the 
presented  environment  which  is  actually  the  subject  and  the 
real  substantive  of  which  this  whole  complex  is  indirectly 
asserted.  If  you  deny  this,  then  show  me  where  you  draw 
your  line,  and  what  point  it  is  in  the  scale  of  judgments  at 
which  the  idea  takes  the  place  of  the  sensible  fact,  and 
becomes  the  true  subject.  And  confine  the  assertion  to  mere 
ideas.  Take  the  ideal  elements  of  a  cow  and  a  hawthorn  tree 
and  a  milk-fnaid,  and  combine  them  ideally  in  any  way  you 
please.  Then  after  they  are  combined,  stand  in  presence  of  the 
fact,  and  ask  yourself  if  that  does  not  enter  into  your  judg- 
ment. If,  with  the  fact  before  you,  you  begin  to  reflect,  you 
will  find  that,  if  you  keep  to  mere  ideas,  you  remove  from  the 
assertion  just  the  thing  you  mean.  In  §  20  we  shall  return  to 
this  point,  but  at  present  we  may  deal  with  a  popular  error. 

§   17.  There   is   a  curious  illusion,  now  widely  spread,  on 


Chap.  II.]  FORMS   OF  JUDGMENT.  59 

the  subject  of  proper  names.  We  find  it  laid  down  that  a 
proper  name  has  not  got  comiotation,  or,  to  use  the  more 
common  technical  term,  it  has  no  intension.  In  ordinary- 
language,  it  stands  for  something  but  does  not  mean  anything. 
If  this  were  true,  it  would  be  hard  to  understand  what  is 
signified  by  such  judgments  as  "John  is  asleep."  There  are 
thinkers  indeed,  who  fear  no  consequence,  and  who  will  tell  us 
that  here  the  name  John  is  the  subject  of  the  proposition.  And 
against  these  adversaries  I  confess  I  have  no  heart  to  enter 
the  lists.  They  may  say  what  they  please  without  hindrance 
from  me.  But,  if  we  are  inclined  to  accept  a  less  heroic 
solution,  and  to  suppose  the  man  John  to  be  the  subject  of  the 
judgment,  then  I  do  not  quite  see  the  purpose  of  the  name,  if 
we  are  not  to  mean  by  it  anything  at  all.  Why  not  simply 
omit  it,  and,  pointing  to  the  man,  say  the  word  "  asleep  "  ? 

"  But  it  stands  for  the  man,"  I  shall  hear  the  reply,  "  and, 
even  when  he  is  present,  it  is  a  mark  which  serves  to  distin- 
guish him  much  more  clearly  than  pointing."  But  that  is 
just  what  puzzles  me.  If  there  is  an  idea  conveyed  by  the 
name,  whenever  it  is  used,  then  it  surely  means  something,  or, 
in  the  language  which  pleases  you,  it  must  be  "  connotative." 
But  if,  on  the  other  hand,  it  conveys  no  idea,  it  would  appear 
to  be  some  kind  of  interjection.  If  you  say  that,  like  "  this  " 
and  "  here,"  it  is  merely  the  ideal  equivalent  of  pointing,  then 
at  once  it  assuredly  has  a  meaning,  but  unfortunately  that 
meaning  is  a  vague  universal.  For  anything  and  everything  is 
"  this  "  and  "  here."  But  if  you  asseverate  that  it  is  the  ideal 
counterpart  of  pointing  in  particular  to  John,  then  you  must 
allow  me  to  doubt  if  you  comprehend  what  you  are  saying. 

;  The  word  "mark"  has  two  senses  which  perhaps  we  may 
confuse.  It  is  something  which  may  be  made  a  means  of 
distinction,  or  something  which  has  been  made  such  a  means.  ' 
I  suppose,  for  I  can  do  no  more  than  suppose,  that  mark  is 
not  taken  in  the  former  sense,  and  that  our  man  was  not  seen 
to  be  distinct  from  other  men,  because  he  was  found  to  have 
the  marking  John.  But,  if  it  is  the  latter  of  these  senses  we 
adopt,  then  a  name  is  a  mark  because  it  is  a  sign,  and  mark 
and  sign  are  here  identical. 
'  Now    a   sign  can  not   possibly  be    destitute  of  meaning. 


60  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

Originally  imposed  as  an  arbitrary  mark,  that  very  process, 
which  makes  it  a  sign  and  associates  it  firmly  with  the  thing 
it  signifies,  must  associate  with  it  also  some  qualities  and 
characters  of  that  which  it  stands  for.  If  it  did  not  to  some 
extent  get  to  mean  the  thing,  it  never  could  get  to  stand  for  it 
at  all.  i  And  can  any  one  say  that  a  proper  name,  if  you  are 
aware  of  its  designation,  brings  no  ideas  with  it,  or  that  these 
ideas  are  mere  chance  conjunction  ?  What  connection,  I  would 
ask,  would  be  left  between  the  bare  name  and  the  thing  it 
stands  for,  if  every  one  of  these  ideas  were  removed  ?  All 
would  vanish  together. 

The  matter  is  so  plain  I  do  not  know  how  to  explain  it. 
The  meaning  of  a  sign  need  of  course  not  be  fixed.  But  is 
the  thing  it  stands  for  quite  invariable  ?  If  the  "  connotation  " 
is  unsteady,  does  the  "  denotation  "  never  change  1  But  where 
the  latter  is  fixed  there  the  former  on  its  side  (within  limits)  is 
stationary.  You  may  have  no  idea  what  "  William  "  connotes, 
but  if  so  you  can  hardly  know  what  it  stands  for.  The  whole 
question  arises  from  a  simple  mistake  and  misunderstanding. 

§  1 8.  "But  after  all  the  name  is  the  sign  of  an  individual, 
and  meanings  are  generic  and  universal.  Therefore  the  name 
can  not  have  any  content  of  which  it  is  the  sign."  I  have 
purposely  put  an  objection  in  that  form  which  suggests  the 
conclusion  I  wish  to  arrive  at.  The  name  of  a  man  is  the 
name  of  an  individual,  which  remains  amid  changing  par- 
ticulars, and  therefore  no  judgment  about  such  an  individual 
is  wholly  analytic.  It  transcends  the  given,  it  becomes  syn- 
thetic, and  with  it  we  pass  into  the  second  great  division  of 
singular  judgments. 

Proper  names  have  a  meaning  which  always  goes  beyond 
the  presentation  of  the  moment.  It  is  not  indeed  true  that 
such  names  must  stand  for  objects,  which  endure  through  a 
train  of  altering  perceptions.  The  unique  thing  they  designate 
may  appear  but  once,  as  an  event  shut  up  within  one  presen- 
tation. But  that  object  would  not  be  unique,  nor  proper  to  its 
own  especial  self,  if  it  did  not  involve  a  reference  to  a  series 
from  which  it  was  excluded.  And  mere  analysis  of  sense 
could  never  suggest  that  limiting  relation  which  gives  it 
uniqueness. 


Chap.  II.J  FORMS   OF  JUDGMENT.  6 1 

And,  when  we  take  the  proper  names  of  objects  which  last 
and  which  reappear,  then  the  given  is  transcended  in  a  still 
higher  sense.  The  meaning  of  such  a  name  is  universal,  and 
its  use  implies  a  real  universality,  an  identity  which  transcends 
particular  moments.  For,  unless  the  person  were  recognized 
as  distinct,  he  would  hardly  get  a  name  of  his  own,  and  his 
recognition  depends  on  his  remaining  the  same  throughout 
change  of  context.  We  could  not  recognize  anything  unless 
it  possessed  an  attribute,  or  attributes,  which  from  time  to  time 
we  are  able  to  identify.  The  individual  remains  the  same 
amid  that  change  of  appearance  which  we  predicate  as  its 
quality.  And  this  implies  that  it  has  real  identity.  Its 
proper  name  is  the  sign  of  a  universal,  of  an  ideal  content 
which  actually  is  in  the  real  world. 

This  assumption,  and  the  practice  of  giving  proper  names, 
may  no  doubt  be  indefensible.  What  concerns  us  here  is 
that  the  practice  transcends  presented  reality.  In  "John  is 
asleep,"  the  ultimate  subject  can  not  be  the  real  as  it  is  now 
given  ;  for  "  John  "  implies  a  continuous  existence,  not  got  by 
mere  analysis.  We  have  reached  the  class  of  synthetic 
judgments. 

§19.  II.  In  this  second  class  of  singular  judgments  (  §  7), 
we  make  generally  some  assertion  about  that  which  appears 
in  a  space  or  time  that  we  do  not  perceive,  and  we  predicate 
of  a  presentation  something  not  got  by  analysis  of  its  content. 
If  I  say  "  There  is  a  garden  on  the  other  side  of  that  wall,'' 
the  judgment  is  synthetic,  for  it  goes  beyond  perception.  And 
in  "  Yesterday  was  Sunday,"  "  William  conquered  England," 
"  Next  month  is  June,"  I  certainly  do  not  analyze  what  is 
merely  given.  In  synthetic  judgments  there  is  always  an 
inference,  for  an  ideal  content  is  connected  with  the  sensible 
qualities  that  are  given  us.  In  other  words  we  have  always 
a  construction,  which  depends  on  ideas,  and  which  only  in- 
directly is  based  on  perception  (vid.  Book  IL). 

And,  this  being  so,  it  seems  as  if  now  we  were  unable  to 
proceed.  If  the  subject  is  the  real  that  appears  in  perception, 
how  can  events  in  the  past  and  future,  or  a  world  in  space  outside 
the  presentation,  and  how  even  can  qualities  not  given  to  sense 
be  referred  to  the  object  and  considered  as  its  adjectives  ?     We 


62  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

have  already  glanced  at  the  solution  of  this  problem,  and  what 
we  now  wish  to  show  is  the  following.  In  synthetic  judgments 
the  ultimate  subject  is  still  the  reality.  That  is  not  the  same 
as  the  momentary  appearance,  and  yet  synthetic  judgments 
are  possible  only  by  being  connected  with  what  is  given  at 
this  very  instant.  The  ideas  of  past  and  future  events  are 
projected  from  the  base  of  present  perception.  It  is  only  in 
that  point  that  they  encounter  the  reality  of  which  they  wish 
to  be  true. 

"  But  past  and  future,"  the  reader  may  object,  "  are  surely 
realities."  Perhaps  they  are,  but  our  question  is.  Given  a 
synthesis  of  ideas  within  my  mind,  how  and  where  am  I  able 
to  get  at  a  reality  to  which  to  attribute  them  ?  How  am  I  to 
judge  unless  I  go  to  presentation  ?  Let  the  past  and  future 
be  as  real  as  you  please,  but  by  what  device  shall  I  come  in 
contact  with  them,  and  refer  to  them  my  ideas,  unless  I 
advance  directly  to  the  given,  and  to  them  indirectly }  It  is 
possible,  I  am  aware,  to  assert  that  past  realities  are  directly 
presented,  and  possible  also  (for  all  I  know)  to  say  the  same 
of  the  future,  and  of  all  the  space  I  am  not  in  contact  with, 
and  of  all  the  qualities  that  I  do  not  perceive.  In  this  way, 
no  doubt,  we  dispose  of  the  difficulty,  and  indeed  may  make 
a  very  simple  matter  of  any  kind  of  problem,  if  indeed  any 
problems  any  longer  will  exist. 

§  20.  But  the  persons  I  write  for,  and  who  are  not  so 
blessed  with  easy  intuitions,  will  feel  this  difficulty,  and  there 
may  come  a  temptation  to  fall  back  once  more  on  the  aban- 
doned heresy  and  to  say,  In  these  synthetic  judgments  the 
subject  cannot  possibly  be  the  reality.  It  must  be  an  idea, 
and  in  the  junction  of  ideas  must  lie  the  truth.  And  I  think, 
perhaps,  at  the  cost  of  repetition,  we  had  better  see  where 
this  temptation  leads  us. 

When  we  say  "  It  rained  last  Tuesday,"  we  mean  tkis  last 
Tuesday,  and  not  any  other,  but,  if  we  keep  to  ideas,  we  do 
not  utter  our  meaning.  (  Nothing  in  the  world  that  you  can 
do  to  ideas,  no  possible  torture  will  get  out  of  them  an  asser- 
tion that  is  not  universal.  We  can  not  escape  by  employing 
ideas  of  events  in  time,  particulars  as  we  call  them.  The 
event  you  describe  is  a  single   occurrence,  but  what  you  say 


Chap.  II.]  FORMS   OF  JUDGMENT.  6$ 

of  it  will  do  just  as  well  for  any  number  of  events,  imaginary 
or  real.  If  you  keep  to  ideas  it  is  useless  to  make  a  reference 
to  the  present,  and  say,  "  The  Tuesday  that  came  before  fkis 
day."  For  we  have  seen  before  (§  8),  that  in  analytic  judg- 
ments we  are  equally  helpless.  The  real  is  inaccessible  by 
way  of  ideas.  In  attempting  to  become  concrete  and  special, 
you  only  succeed  in  becoming  more  abstract  and  wholly  in- 
definite. "This"  *'now  "  and  "mine"  are  all  universals.  And 
your  helpless  iteration,  "  not  this  but  this,"  will  not  get  your 
expression  any  nearer  to  your  meaning.  If  judgment  is  only 
the  union  of  ideas,  no  judgment  is  ever  about  the  individual. 

§  21.  We  must  get  rid  of  the  erroneous  notion  (if  we  have 
it)  that  space  and  time  are  "  principles  of  individuation,"  in  the 
sense  that  a  temporal  or  spatial  exclusion  will  confer  unique- 
ness upon  any  content.  It  is  an  illusion  to  suppose  that,  by 
speaking  of  "  events,"  we  get  down  to  real  and  solid  particulars, 
and  leave  the  airy  region  of  universal  adjectives.  For  the 
question  arises.  What  space  and  time  do  we  really  mean,  and 
how  can  we  express  it  so  as  not  to  express  what  is  as  much 
something  else  }  It  is  true  that,  in  the  idea  of  a  series  of  time 
or  complex  of  space,  uniqueness  is  in  one  sense  involved  ;  for 
the  parts  exclude  one  another  reciprocally.  But  they  do  not 
exclude,  unless  the  series  is  taken  as  one  continuous  whole, 
and  the  relations  between  its  members  are  thus  fixed  by  the 
unity  of  the  series.  Apart  from  this  unity,  a  point  on  its  recur- 
rence could  not  be  distinguished  from  the  point  as  first  given. 
And  elsewhere  we  might  ask,  how  far  such  an  unity  is  itself 
the  negation  of  mere  exclusivity. 

But,  to  pass  by  this  question,  it  is  clear  that  exclusion 
within  a  given  series  does  not  carry  with  it  an  absolute  unique- 
ness. There  is  nothing  whatever  in  the  idea  of  a  series  to 
hint  that  there  may  not  be  any  number  of  series,  internally  all 
indistinguishable  from  the  first.  How  can  you,  so  long  as  you 
are  not  willing  to  transcend  ideas,  determine  or  in  any  way 
characterize  your  series,  so  as  to  get  its  difference  from  every 
possible  series  within  your  description  .?  It  is  idle  to  say  "  this," 
for  "  this  "  does  not  exclude  except  in  tMs  sphere,  and  it 
is  idle  to  say  "  my,"  for  it  is  only  in  mf  element  that  yours 
and  mine  collide.     Outside  it  they  are  indifferent,  and  the  ex- 


64  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

pression  "  my  "  will  not  distinguish  one  world  from  the  other. 
If  we  simply  attend  to  the  series  itself,  and  declining  to  look 
outside,  confine  ourselves  to  the  consideration  of  its  character, 
then  all  that  it  contains  might  be  common  property  of  innu- 
merable subjects,  existing  and  enjoyed  in  the  world  of  each,  a 
general  possession  appropriated  by  none.  The  mere  quality 
of  appearance  in  space  or  time  can  not  give  singularity. 

§  22.  The  seeking  for  judgment  in  the  synthesis  of  ideas 
once  more  has  led  us  where  there  is  no  exit.\  With  however 
little  hope  we  must  return  to  the  doctrine,  that  judgment  is 
the  reference  of  an  ideal  content  to  the  real  which  appears  in 
time  and  space,  which  is  to  be  encountered  directly  in  presen- 
tation, but  which  can  not  be  limited  to  a  momentary  instance. 
It  is  not  by  its  quality,  as  a  temporal  event  or  phenomenon  of 
space,  that  the  given  is  unique.  It  is  unique,  not  because  it 
has  a  certain  character,  but  because  it  is  given.  It  is  by  the 
reference  of  our  series  to  the  real,  as  it  appears  directly  within 
this  point  of  contact,  or  indirectly  in  the  element  continuous 
with  this  point,  that  these  series  become  exclusive.  We 
perhaps  may  be  allowed  to  express  this  otherwise  by  saying, 
it  is  only  the  "  this  "  which  is  real,  and  ideas  will  suffice  so  far 
as  "  thisness,"  but  can  never  give  "  this."  It  is  perhaps  a  hard 
saying,  and  announces  difficulties  we  shall  need  both  courage 
and  patience  to  contend  with. 

§  23.  Everything  that  is  given  us,  all  psychical  events,  be 
they  sensations,  or  images,  or  reflections,  or  feelings,  or  ideas, 
or  emotions — every  possible  phenomenon  that  can  be  present — 
both  is  "  this  "  and  has  "  thisness."  But  its  stamp  of  uniqueness 
and  singularity  comes  to  it  from  the  former  and  not  from  the 
latter.  If  we  distinguish  the  aspects  of  existence  and  content 
(Chap.  I.  §  4),  and  put  on  the  one  side  that  anything  is,  and 
on  the  other  side  what  it  is,  then  the  thisness  falls  within  the 
content,  but  the  this  does  not  fall  there.  It  is  the  mere  sign 
of  my  immediate  relation,  my  direct  encounter  in  sensible 
presentation  with  the  real  world.  I  will  not  here  ask  how 
"  this  "  is  related  to  existence,  how  far  it  holds  of  the  actual 
fact,  and  how  far  only  of  the  mere  appearance ;  whether  it  is 
or  is  only  for  me.  Apart  from  that,  at  least  so  much  is  cer- 
tain, that  we  find  uniqueness  in  our  contact  with  the  real,  and 


Chap.  II.]  FORMS   OF  JUDGMENT.  65 

that  we  do  not  find  it  anywhere  else.  This  singularity  which 
comes  with  presentation  and  is  what  we  call  "  this,"  is  not  a 
quality  of  that  which  is  given. 

But  thisness  on  the  other  hand  does  belong  to  the  content, 
and  is  the  general  character  of  every  appearance  in  space  or 
time.  Thisness,  if  we  like,  we  may  call  particularity.  Every- 
thing that  is  given  us  is  given,  in  the  first  place,  surrounded 
and  immersed  in  a  complex  detail  of  innumerable  relations  to 
other  phenomena  in  space  or  time.  In  its  internal  quality 
we  find  again  a  distinction  of  aspects,  which  we  always  can 
carry  to  a  certain  length,  and  can  never  be  sure  we  have  quite 
exhausted.  And  the  internal  relations  of  its  component 
elements  in  space  or  time  are  again  indefinite.  We  are  never 
at  the  end  of  them.  This  detail  appears  to  come  to  us  on 
compulsion  ;  we  seem  throughout  to  perceive  it  as  it  is,  and 
in  no  sense  to  make  or  even  to  alter  it.  And  this  detail  it  is 
which  constitutes  thisness,* 

But  such  particularity  in  space  or  time,  such  an  exclusive 
nature,  after  all,  is  only  a  general  character.  It  falls  in  the 
content  and  does  not  give  the  existence.  It  marks  the  sort 
but  it  misses  the  thing.  In  abstraction  from  the  this  it  is 
merely  ideal,  and,  apart  from  the  this,  ideas  as  we  know  can 
not  reach  to  uniqueness.  No  amount  of  thisness  which  an 
event  possesses  will  exclude  the  existence  of  self-same  events 

*  The  apprehension  of  this  character,  it  may  be  objected,  takes  time, 
and,  if  any  time  for  observation  is  given,  the  product,  for  all  we  know, 
has  been  altered.  But  this  difficulty  occurs  in  all  observation.  We 
everywhere  assume,  first,  that  things  are  not  different  unless  we  can 
discriminate  them.  And  we  assume,  in  the  second  place,  our  ability  to 
distinguish  a  change  in  ourselves  from  a  change  in  the  object.  We 
assume  that  more  of  the  same  object  is  observed,  unless  we  have  reason 
either  to  suppose  that  our  fancy  has  wandered  away  from  that  object, 
or  that  the  object  itself  has  undergone  a  change.  I  do  not  here  ask  if 
these  assumptions  are  valid.  But  I  may  remark  in  passing,  that  the 
doubt  if  in  introspection  we  examine  a  present,  or  only  a  past  state  of 
mind,  should  change  its  form.  It  should  not  take  the  two  as  exclusive 
here,  unless  it  faces  the  same  problem  elsewhere.  For  the  observation 
of  external  phenomena  labours  under  the  identical  difficulty.  If  an 
internal  fact  can  not  possibly  be  both  present  a7id  past,  then  an  external 
fact  must  be  likewise  restricted.  The  two  kinds  of  observation  are  not 
essentially  different.  External  facts  are  not  absolutely  fixed,  nor  are 
internal  facts  in  absolute  flux. 


66  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

in  other  like  series.  Such  exclusiveness  falls  all  within  the 
description,  and  that  which  is  only  of  this  description  is  simply 
such_and^an  not  be  this. 

In  every  judgment,  where  we  analyze  the  given,  and  where 
as  the  subject  we  place  the  term  "  this,"  it  is  not  an  idea  which 
is  really  the  subject.  In  using  "this"  we  do  nse  an  idea,  and 
that  idea  is  and  must  be  universal ;  but  what  we  mean,  and 
fail  to  express,  is  our  reference  to  the  object  which  is  given  as 
unique. 

§  24.  And  here  we  encounter  an  awkward  question.  The 
reader  possibly  may  be  willing  to  accept  our  account  of  this- 
ness.  He  may  agree  that,  so  far  as  in  our  use  of  the  term  we 
mean  mere  relativity  in  space  or  time,  in  other  words  particu- 
larity, we  do  not  at  all  go  beyond  the  content.  And  he  may 
allow  the  consequence  that  we  have  so  an  idea  which  is  only 
universal.  But  in  using  "  this,"  he  may  go  on  to  object  that 
we  have  in  addition  another  idea.  We  have  the  idea  of  imme- 
diate contact  with  the  presented  reality :  and  it  is  that  idea 
which  is  signified  by  "  this,"  and  which  qualifies  the  idea  which 
stands  as  the  subject  of  our  analytic  judgment. 

We  answer.  Assuredly,  if  such  were  the  case,  the  reference 
to  fact  would  inevitably  and  always  fall  outside  the  judgment. 
Once  again  we  should  be  floating  in  the  air,  and  never  be  more 
than  hypothetical.  But  the  question  raised  need  not  so  be 
dismissed,  for  it  leads  to  an  interesting  if  subtle  reflection. 
The  idea  of  "  this,"  unlike  most  ideas,  can  not  be  used  as  a 
symbol  in  judgment. 

It  is  certain,  in  the  first  place,  that  we  have  the  idea. 
Indeed  we  could  scarcely  deny  that  we  had  it,  unless  in  so 
doing  we  actually  used  it.  Beside  the  idea  of  exclusion  in  a 
series,  which  is  mere  thisness,  we  have  also  the  idea  of  my 
immediate  sensible  relation  to  reality,  and,  if  so,  we  have 
"  this."  We  are  able  to  abstract  an  idea  of  presence  from  that 
direct  presentation  which  is  never  absent ;  and  presence, 
though  it  does  not  fall  within  the  content,  though  we  can 
hardly  call  it  a  quality  of  the  appearance,  yet  is  recognized  as 
the  same  amid  a  change  of  content,  is  separable  from  it,  and 
makes  a  difference  to  !t.  Thus  ideally  fixed  "  this  "  becomes 
an  universal  among  other  universals. 


Chap.  IL]  FORMS   OF  JUDGMENT.  6/ 

§  25.  But,  despite  the  likeness,  it  is  very  different  from  an 
ordinary  idea.  Ideas,  we  shall  remember,  are  used  as  symbols 
(Chap.  I.).  In  my  idea  of  "  horse  "  we  have  (i)  the  existence 
of  an  image  in  my  head,  (ii)  its  whole  content,  and  (iii)  its 
meaning.  In  other  words  we  may  always  distinguish  (i)  that 
it  is,  and  (ii)  what  it  is,  and  (iii)  what  it  signifies.  The  two 
first  of  these  aspects  belong  to  it  as  a  fact.  The  third  is  the 
universal  which  does  not  belong  to  it,  but  is  thought  of 
without  a  relation  to  its  existence,  and  in  actual  judgment  is 
referred  away  to  some  other  subject. 

The  idea  of  "  this  "  has  a  striking  difference.  Distinguished 
as  an  aspect  of  presented  reality,  when  we  call  it  up  we  take 
any  perception  or  feeling  that  is  given,  and,  attending  to  the 
aspect  of  presence  within  it,  recognize  that  as  the  meaning  of 
our  term.  We  contemplate  it  ideally,  without  any  reference 
to  the  content  of  that  which  is  actually  before  us. 

But  how  shall  we  fare  when,  attempting  a  judgment,  we 
attribute  the  adjective  we  have  so  cut  loose  to  another  sub- 
stantive ?  It  is  here  we  are  stopped.  For  any  judgment  so 
made  we  discover  must  be  false.  The  other  fact  can  not  be 
presented  without  ipso  facto  altering  the  given.  It  degrades 
our  given  to  one  element  within  a  larger  presentation,  or  else 
it  wholly  removes  it  from  existence.  The  given  disappears 
and  with  itself  carries  our  idea  away.  We  are  now  unable  to 
predicate  the  idea,  since  we  no  longer  possess  it,  or  if  we  still 
have  it,  then  what  supports  it  excludes  that  other  fact  to 
which  we  wish  to  refer  it. 

§  26.  To  repeat  the  above,  the  presented  instance  of 
reality  is  unique.  By  discrimination  we  are  able  to  fix  that 
uniqueness  in  the  shape  of  an  idea.  We  thereupon  try  to 
make  it  the  idea  of  something  else.  But,  for  the  idea  to  be 
true  of  something  else,  that  something  else  must  be  present 
and  unique.  We  have  then  either  two  unique  presentations, 
or  one  must  disappear.  If  the  first  one  goes  the  idea  goes 
with  it.  If  the  last  one  goes  there  is  now  no  fact  for  the  idea 
to  be  referred  to.  In  either  case  there  can  be  no  judgment. 
The  idea,  we  see,  is  not  the  true  idea  of  anything  other  than 
its  own  reality.  It  is  a  sign  which,  if  we  judge,  can  signify 
nothing  except  itself     To    be  least   alone    then  when  most 

F   2 


68  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

alone,  and  to  enjoy  the  delights  of  solitude  together,  are 
phrases  which  have  a  very  good  sense  :  but,  taken  in  their 
bare  and  literal  meaning,  they  would  exemplify  the  contradic- 
tion we  have  here  before  us. 

Between  the  fact  and  the  idea  of  the  "  this  "  in  judgment 
there  can  be  no  practical  difference.  The  idea  of  this  would 
be  falsely  used,  unless  what  it  marks  were  actually  presented. 
But  in  that  case  we  should  be  trying  to  use  a  sign,  when  we 
have  before  us  the  fact  which  is  signified.  We  can  use  the 
idea  so  far  as  to  recognize  the  fact  before  us  as  a  fact  which 
is  "  this  ; "  but  such  a  use  does  not  go  beyond  the  given.  It 
affirms  of  the  subject  a  predicate  without  which  the  subject 
disappears.  It  implies  discrimination  within  the  fact  in  which, 
since  the  aspect  discriminated  is  not  separable  from  the  given, 
that  given  with  its  aspect  still  remains  as  the  subject.  So 
that  the  addition  of  the  idea  adds  nothing  to  the  subject. 
And  if  again  it  were  possible  to  import  the  idea  from  the 
content  of  another  fact,  the  operation  would  be  uncalled  for 
and  quite  inoperative. 

And  it  is  not  possible.  It  would  be,  as  we  have  seen,  the 
attempt  to  have  before  us  two  unique  facts  at  once.  What 
we  mean  by  "this"  is  the  exclusive  focus  of  presentation 
which  lights  up  its  content,  and  it  is  of  that  singular  content 
that  we  use  the  idea.  And  to  treat  that  idea  as  a  meaning 
which  could  be  true  elsewhere,  would  be  to  bring  into  our 
focus  another  content.  But  since  both  must  be  unique,  as  well 
as  the  same,  a  dilemma  arises  which  we  need  not  draw  out. 

§  27.  And  if  "  this  "  be  used  in  a  different  sense,  if  it  does 
not  mark  the  presence  of  the  whole  sensible  detail  that  falls 
within  the  focus  ;  if  it  is  used  for  that  which  I  specially  attend 
to,  the  result  will  be  the  same.  If  I  make  A  my  object  to 
the  exclusion  of  all  others,  then  this  special  relation  to  myself 
must  be  false,  if  used  of  any  other.  If  applied  to  A  it  can  not 
possibly  also  be  applied  to  B. 

"  But,"  it  may  be  said,  "  I  exclusively  attend  to  both.  A 
and  B  are  both  elements  within  the  given  '  this,'  and  hence  I 
can  predicate  '  this  '  of  either.  I  can  transfer  the  idea,  which  I 
find  is  true  of  one,  and  use  it  as  a  predicate  which  is  true  of 
the  other.     And  so,  after  all,  the  idea  of  '  this,'  will  be  used 


Chap.  IL]  FORMS   OF  JUDGMENT.  69 

symbolically."  I  am  afraid  of  losing  the  main  question  in 
subtleties,  but  I  must  reply  by  pointing  out  a  confusion. 
Since  A  and  B  are  both  taken  together,  you  can  not  ex- 
clusively deal  with  each  separately.  So  much  is  now  clear. 
But,  on  the  other  hand,  if  you  take  each  by  itself  as  a  mere 
element  in  the  "  this,"  then  you  can  not  predicate  "  this  "  of 
either.  Both  will  belong  to  the  "  this,"  but  neither  will  be  that 
to  which  they  belong.  They  will  be  presented,  but  neither 
by  itself  will  be  the  unique  presentation.  They  will  not  have 
the  "this"  in  common,  but  the  "this"  will  have  them.  It 
will  be  their  common  substantive  which  will  share  its  own 
exclusive  nature  with  nothing. 

I  hardly  think  that  by  further  intricacies  we  shall  make 
more  clear  what  can  not  be  made  obvious.  If  anything  in  the 
above  has  been  grasped  by  the  reader,  I  trust  to  have  shown 
that  the  use  of  "  this,"  as  a  symbol  in  judgment,  is  not  only 
impossible,  but  that,  if  it  existed,  it  would  be  wholly  nugatory.* 

§  28.  We  escape  from  ideas,  and  from  mere  universals,  by 
a  reference  to  the  real  which  appears  in  perception.  It  is  thus 
our  assertion  attains  the  uniqueness  without  which  it  would 
not  correspond  to  the  fact.  And  analytic  judgments,  it  may 
seem,  are  thus  secured  to  us.  But  now,  when  we  return  to 
the  question  we  asked  in  §  19,  and  when  we  pass  to  judgments 
that  are  synthetic,  and  extend  to  spaces  and  times  not 
falling  within  the  radius  of  direct  presentation,  we  seem  at 
first  sight  to  be  no  better  off.  What  we  have  gained,  it  may 
now  appear,  has  been  at  the  expense  of  everything  beyond. 
The  series  of  all  our  spaces  and  times  will  now  have  to  be 
referred  to  the  one  unique  point  of  contact  with  reality.  It  is 
only  so  that  their  content  can  be  stamped  with  the  mark  of 
fact.     But  it  seems  impossible  to  establish  this  relation. 

The   content   of  these   synthetic   assertions   we    know    is 

*  "  This  "  is  not  the  only  idea  which  can  never  be  true  as  a  symbol, 
I  will  not  ask  to  what  extent  "  this  "  means  "  for  me,"  but  what  has  been 
said  of  "  this  "  will  hold  in  the  main  of  "  I  "  "  me  "  and  "  mine."  But  there 
are  difficulties  here  which  we  can  not  discuss.  We  may  remark  in  passing 
that,  for  the  purposes  of  metaphysics,  it  would  be  necessary  to  find  all 
those  ideas  whose  content  appears  not  able  to  be  used  as  the  adjective 
of  something  else.  This  would  bear  on  the  so-called  "  ontological  proof" 
For  the  ideas  of  uniqueness,  &c.,  vid.  infr.  §§  38,  39. 


70  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

universal.  It  may  be  true  of  innumerable  other  series.  This 
unsubstantial  chain,  if  left  to  itself,  does  not  touch  the  ground 
in  any  one  point.  On  the  other  hand,  the  given  source  of 
reality  refuses,  it  seems,  to  have  anything  to  do  with  these 
floating  threads.  Their  symbolic  content  can  not  be  directly 
attributed  to  the  presentation,  because  it  is  irreconcileable 
with  the  content  of  that.  And,  if  we  can  not  have  another 
presentation,  where  is  the  fact  in  connection  with  which  our 
universals  can  attain  reality  .? 

§  29.  We  must  turn  in  our  difficulty  to  a  result  we  got 
from  a  former  discussion.  We  saw  that  the  real,  which 
appears  in  perception,  is  not  identical  with  the  real  just  as  it 
appears  there.  If  the  real  must  be  "  this,"  must  encounter  us 
directly,  we  can  neither  conclude  that  the  "this"  we  take  is 
all  the  real,  or  that  nothing  is  real  beyond  the  "  this."  It  is 
impossible,  perhaps,  to  get  directly  at  reality,  except  in  the 
content  of  one  presentation  :  we  may  never  see  it,  so  to  speak, 
but  through  a  hole.  But  what  we  see  of  it  may  make  us 
certain  that,  beyond  this  hole,  it  exists  indefinitely.  If  by 
"  this  "  we  understand  unique  appearance,  then,  as  "  this  "  was 
not  any  part  of  the  content,  so  neither  is  it  any  quality  of  the 
real,  in  such  a  sense  as  to  shut  up  the  real  within  that  quality. 
It  would  belong  to  metaphysics  to  discuss  this  further,  and  we 
must  here  be  content  with  a  crude  result.  The  real  is  what 
appears  to  me.  The  appearance  is  not  generic  but  unique. 
But  the  real  itself  is  not  unique,  in  the  sense  in  which  its 
appearance  is  so. 

The  reality  we  divined  to  be  self-existent,  substantial,  and 
individual :  but,  as  it  appears  within  a  presentation,  it  is  none 
of  these.  The  content  throughout  is  infected  with  relativity, 
and,  adjectival  itself,  the  whole  of  its  elements  are  also 
adjectival.  Though  given  as  fact  every  part  is  given  as 
existing  by  reference  to  something  else.  The  mere  perpetual 
disappearance  in  time  of  the  given  appearance  is  itself  the 
negation  of  its  claim  to  self-existence.  And  again,  if  we  take 
it  while  it  appears,  its  limits,  so  to  speak,  are  never  secured 
from  the  inroads  of  unreality.  In  space  or  in  time  its  outside 
is  made  fact  solely  by  relation  to  what  is  beyond.  Living  by 
relation  to  what  it  excludes,  it  transcends  its  limits  to  join 


TJNIvERi^ii^l 


Chap.  II.]  FORMS   OF  JUDGMENT. 

another  element,  and  invites  that  element  within  its  own 
boundaries.  But  with  edges  ragged  and  wavering,  that  flow 
outward  and  inward  unstably,  it  already  is  lost.  It  is 
adjectival  on  what  is  beyond  itself.  Nor  within  itself  has  it 
any  stability.  There  is  no  solid  point  of  either  time  or  space. 
Each  atom  is  merely  a  collection  of  atoms,  and  those  atoms 
again  are  not  things  but  relations  of  elements  that  vanish. 
And  when  asked  what  is  ultimate,  and  can  stand  as  an 
individual,  you  can  answer  nothing. 

The  real  can  not  be  identical  with  the  content  that  appears 
in  presentation.  It  for  ever  transcends  it,  and  gives  us  a  title 
to  make  search  elsewhere. 

§  30.  The  endeavour  to  find  the  completeness  of  the  real, 
which  we  feel  can  not  exist  except  as  an  individual,  will  lead 
us  first  to  Synthetic  judgments  of  time  and  space.  But, 
before  we  proceed,  we  may  pause  for  a  moment,  to  reflect  on 
the  general  nature  of  the  attempt.  If  the  reality  is  self- 
existent,  self-contained,  and  complete,  it  needs,  one  would 
think,  no  great  eflbrt  of  reason  to  perceive  that  this  character 
is  not  to  be  found  in  a  mere  series  of  phenomena.  It  is  one 
thing  to  seek  the  reality  m  that  series  :  it  is  quite  another 
thing  to  try  to  find  as  the  series.  A  completed  series  in  time 
or  space  can  not  possibly  exist.  It  is  the  well-known 
phantasm  of  the  spurious  infinitej  a  useful  fiction,_it  may  be, 
for  certain  purposes  and  at  certain  levels  of  thought,  but 
none  the  less  a  phantasm  which,  until  it  is  recognized,  stops 
the  way  of  all  true  philosophic  thought.  It  emerges  often  in 
the  school  of  "  experience,"  in  its  Logic  and  again  in  its 
Hedonistic  Ethics,  where  it  begets  and  will  continue  to  beget 
chimseras.  We  shall  meet  it  again  in  the  present  chapter,  but 
must  return  to  our  search  for  reality  within  a  series  of 
phenomena,  a  search  not  yet  degraded  to  a  pursuit  of 
phantasms,  but  carrying  in  itself  the  root  of  illusion. 

§  31.  The  real  then  itself  transcends  the  presentation,  and 
invites  us  to  follow  it  beyond  that  which  is  given.  On  the 
other  hand,  we  seem  to  find  contact  with  reality  and  to  touch 
ground  nowhere,  so  to  speak,  outside  the  presented.  How 
then  is  a  content  to  be  referred  to  the  real,  if  it  can  not  be 
referred  to  the  real  as  perceived  }     We  must  answer  that  the 


72  THE   PRINCIPLES  OF  LOGIC.  [Book  L 

content  is  referred  indirectly.  It  is  not  attributed  to  the  given 
as  such  ;  but,  by  establishing  its  connection  with  what  is 
presented,  it  is  attributed  to  the  real  which  appears  in  that 
given.  Though  it  is  not  and  can  not  be  found  in  presentation, 
it  is  true  because  it  is  predicated  of  the  reality,  and  unique 
because  it  is  fixed  in  relation  with  immediate  perception. 
The  ideal  world  of  spaces  beyond  the  sensible  space,  and  of 
times  not  present  but  past  and  future,  fastens  itself  on  to  the 
actual  world  by  fastening  itself  to  the  quality  of  the  im- 
mediate this.  In  a  single  word  continuity  of  content  is  taken 
to  show  identity  of  element. 

§  32.  But  such  continuity,  and  the  consequent  extension 
of  the  "this"  as  given,  depend,  like  every  other  ideal  con- 
struction, on  identity.  An  inference  always,  we  shall  see 
hereafter,  stands  on  the  identity  of  indiscernibles.  Sameness 
of  quality  proves  real  sameness  (vid.  Book  II.  Part  I.  Chap. 
VI.).  And  the  identity  here  has  a  double  form,  (i)  In  the 
first  place  the  symbolical  content  must  have  "  thisness."  (ii)  In 
the  second  place  it  must  share  some  point  with  the  "  this." 

To  explain,  (i)  the  idea  we  are  to  connect  with  perception 
must  be  the  idea  of  something  in  space  or  some  event  in  time. 
It  must  have  the  character  of  particularity,  the  general  idea  of 
indefinite  detail  and  endless  relation.  We  know  by  this  that 
it  is  of  the  same  sort  as  the  content  of  the  given.  The  de- 
scription of  both  is  one  and  the  same.  They  both  have 
"  thisness,"  and  therefore  their  element  may  be  identical. 

(ii)  But,  so  far  as  we  have  gone,  we  still  are  left  in  the 
world  of  universals,  which  may  or  migUt  touch  the  ground  in 
some  place  and  meet  the  fact  which  appears  in  perception, 
but  which  do  not  certainly  do  thus.  We  wish,  on  the  one  side, 
to  pass  beyond  presented  content,  and,  on  the  other  side,  to 
connect  with  this  content  an  ideal  series  :  and  we  seek  for  a 
link  by  which  to  fasten  them  together. 

That  link  is  found  by  establishing  a  point  which  is  the 
same  in  both,  and  is  the  same  because  its  quality  is  the  same. 
The  "  this "  contains  a  complex  of  detail,  either  times  or 
spaces  (or  both)  in  series,  which  we  may  call  c.  d.  e.f.  The 
idea,  on  its  side,  contains  a  series  of  particulars  a.  b.  c,  d. 
The  identity  of  c.d.  in  each  extends  the  perception  c.  d.  e.  f. 


Chap.  II.]  FORMS   OF  JUDGMENT.  73 

by  the  ideal  spaces  or  times  a.  b.,  and  the  whole  is  given 
by  synthetical  construction  as  a  single  fact  a.  b.  c.  d.  e.  f. 
The  whole  series  now  is  referred  to  the  real,  and  by  the  con- 
nection with  unique  presentation,  has  become  a  series  of  events 
or  spaces,  itself  unique  and  the  same  as  no  other  series  in  the 
world.  It  is  thus  by  an  inference  that  we  transcend  the  given 
through  synthetic  judgments,  and  our  following  Books  must 
explain  more  clearly  the  nature  of  inference,  and  the  enormous 
assumption  on  which  it  reposes. 

§  33.  Mental  pathology  will  afford  an  illustration.  There 
are  cases  where  the  subject  or,  if  we  please,  the  Ego  seems 
divided  in  two.  When  one  self  is  present  the  other  is  absent, 
and  the  memories  of  either  self  are  distinct.  Their  pasts  and 
futures  do  not  ever  touch.  The  explanation  that  is  offered, 
and  which  seems  sufficient,  will  illustrate  our  theme.  It  is 
because  the  present  selves  are  different,  that  the  past  and 
future  selves  are  foreign.  It  is  because  one  system  of  ideas 
has  not  got  a  point  of  connection  with  the  other  system,  or 
has  rather  some  point  which  excludes  the  connection,  that  the 
one  can  never  be  used  to  extend  ideally  a  present  which 
belongs  to  the  other.  Some  mode  of  morbid  feeling  or  diseased 
perception,  given  now  in  presentation,  links  on  to  itself  the 
ideas  that  are  grouped  by  the  same  characteristic.  The  whole 
ideal  region  where  that  colouring  fails,  may  perhaps  be  sug- 
gested, but  can  never  be  fixed  in  continuous  relation  with  the 
present  perception.* 

^  34.  If  we  mean  by  phenomena  the  things  we  perceive, 
or  the  facts  or  appearances  that  are  given  to  us,  then  the  whole 
of  England  below  our  horizon  (to  say  nothing  at  all  of  America 
and  Asia),  and  every  event  that  is  past  or  future  are  not 
phenomena.  They  are  not  perceived  facts.  They  exist  in 
our  minds  as  mere  ideas,  as  the  meaning  of  symbols.  A  phe- 
nomenon, I  repeat,  that  is  past  or  future  is  a  sheer  self-contra- 
diction. It  is  time  we  thought  of  giving  up  our  habit  of  talking 
about  the  "  series  of  phenomena,"  or  "  thread  of  perceptions," 
or  Heaven  knows  what  else,  as  though  we  held  these  facts  in 
our  hands.  One  thing  or  the  other.  Either  a  phenomenon 
may  be  ideal,  the  content  of  a  symbol  and  not  even  predicated 
*  Cf.  Lotze,  Mikrokosmiis^  I.  371. 


74  THE   PRINCIPLES  OF   LOGIC.  [Book  L 

directly  of  the  present  perception,  or  there  is  no  phenomenon 
but  what  I  here  and  now  perceive.  It  is  idle  perhaps  to 
appeal  to  facts  in  protest  against  the  philosophy  of"  analysis  '* 
and  the  school  of  "  experience."  It  is  impossible,  I  know,  to 
persuade  the  man  who  is  wedded  to  these  names,  that  he  has 
failed  to  earn  a  legitimate  title  to  neglect  the  first  and  to  be 
false  to  the  second.  Profuse  protestations,  and  jealousy  of 
the  untitled,  are  services  found  not  too  exacting,  and  which 
satisfy  those  who  have  long  ago  and  cheaply  become  cool. 
But,  for  the  sake  of  others,  I  will  repeat  once  more.  If  a 
fact  or  event  is  what  is  felt  or  perceived,  then  a  fact  that  is 
past  is  simple  nonsense  Jcf  Book  II.  Part  II.  Chap.  I.). 

Of  course,  I  know,  it  is  easy  to  say  that  past  events  are  all 
really  there,  and,  being  there,  are  remembered ;  as  I  presume 
the  future,  being  all  there,  is  anticipated.  But  suppose  that 
there  is  a  series  of  facts,  both  past  and  future,  outside  our 
minds,  the  question  remains  How  can  they  get  in  }  You  may 
say,  if  you  like.  They  are  fond  of  a  change,  and  walk  in  and 
out  bodily  and  meet  and  converse  there.  Or  an  omnipotent 
Creator  has  endowed  the  mind  with  an  extraordinary  organ, 
which  perpetually  can  do  what  no  one  understands,  and,  defy- 
ing the  insidious  arts  of  the  analyst,  proves  by  the  way  the 
immortality  of  the  soul.  Or  perhaps  you  may  find  it  a  "  final 
inexplicability."  Ultimate  facts  always  are  inexplicable,  and 
we  must  not  be  put  out  if  they  contradict  those  doctrines  they 
must  know  to  be  true.  For  it  is  natural  for  the  inexplicable 
to  behave  inexplicably. 

But  perhaps  there  are  readers  content  to  remain  on  a  level 
with  ourselves.  If  so  they  will  continue  to  believe  the  conclu- 
sion the  facts  have  brought  to  us.  rAndThat  conclusion  is  that 
events  past  and  future,  and  all  things  not  perceived,  exist 
for  us  only  as  ideal  constructions  connected,  by  an  inference 
through  identity  of  quality,  with  the  real  that  appears  in 
present  perception.  In  what  character  (if  any)  these  things 
may  really  exist  for  themselves,  is  a  question  for  metaphysics.  ) 

§  35.  Synthetic  judgments  thus  cease  to  be  merely  adjec- 
tival, and  they  express  a  series  of  unique  events  by  indirect 
reference  to  the  real  which  appears  in  unique  presentation. 
They  are  connected  by  an  inference  with  the  content  of  this 


Chap.  II.]  FORMS   OF  JUDGMENT.  75 

appearance,  and  so  far  are  directly  related  to  perception.  But 
their  ideas  are  never  referred  as  adjectives  to  the  presentation 
itself  They  are  attributed  to  the  reality,  which  both  shows 
itself  there,  and  extends  itself  beyond.  The  content  of  our 
perceptions,  and  the  content  of  our  ideal  constructions,  are  both 
the  adjectives  of  one  reality.  They  are  both  appearances, 
which  come  to  us  in  different  ways,  but  which  both  (unless  our 
assumptions  are  false)  are  valid  and  true  of  the  real  world. 

§  36.  Memory  of  the  past,  and  prediction  of  the  future, 
are  separated  clearly  from  mere  imagination.  In  the  former 
we  have  the  reference  to  that  reality  which  appears  in  percep- 
tion. We  have  a  judgment  which  is  either  true  or  false, 
because  it  implies  a  relation  to  fact.  But  imagination  is  with- 
out this  reference.  The  merely  imagined,  we  have  seen  before 
(Chap.  I.  §  14)  may  be  stronger  than  that  which  we  judge  to 
be  true.  What  we  only  fancy  may  have  more  thisness ;  it 
may  have  more  compulsory  and  particular  detail  than  that 
which  we  remember.  But  what  it  wants  is  a  point  of  identity 
by  which  to  fasten  it  on  to  the  "  this."  And  without  such  a 
link  it  must  fall  outside  the  series. 

We  generally,  it  is  true,  take  forcible  detail  and  strong 
particularity  as  a  sign  of  fact,  and  look  for  its  place  in  the 
series  of  events.  But,  if  the  place  is  not  found,  the  imagined 
fact  is  never  secured  to  us.  The  visions  of  dreams  may  be 
very  definite,  but  the  content  of  those  visions  refuses  to  link 
itself  to  the  series  of  events  connected  with  perception,  and  so, 
if  we  can  not  get  rid  of  the  ideas,  at  least  we  stamp  them  as 
mere  illusions. 

If  this  were  the  place  for  an  excursion  into  psychology,  we 
should  find  some  difficulties  and  many  interesting  questions. 
When  once  we  have  referred  a  content  to  the  real,  we  gene- 
rally tend  to  refer  it  again.  We  say  that  we  know  it  happened 
at  some  time,  though  when  we  can  not  say.  And  we  might 
be  tempted  perhaps  to  think  that  such  ideas  have  greater 
strength  or  fuller  detail  than  mere  imaginations.  This  would 
be  erroneous.  It  is  not  strength  or  detail  which  marks  these 
ideas,  but  something  so  dim  that  we  can  not  grasp  it.  It  may 
be  the  general  idea  of  reference  to  the  "  this,"  which,  repelled 
by  the  content  of  the  given  "  this,"  transcends  it  vaguely.    It 


11 


7^  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

may  be,  on  the  other  hand,  some  unconscious  element  of  idea 
or  feeling,  which  serves  to  identify  in  an  indefinite  way  the 
imagined  with  fact.  For  it  is  a  mistake  to  suppose  that  these 
links  with  reality  need  be  anything  explicit.  A  feeling  so 
obscure  that  we  are  not  aware  of  it,  and  which  perhaps  no 
effort  of  attention  would  be  able  to  distinguish  from  its  vague 
totality  of  consciousness,  may  serve  as  the  basis  by  which  we 
separate  a  truth  from  a  fiction  (§  33).  We  must  remember 
again  that  the  point  of  connection  may  be,  so  to  speak,  in  our 
inward  selves,  and  not  at  all  in  the  outward  series.  If  a  false- 
hood imagined  is  in  the  end  believed,  it  is  not  always  because 
it  gains  some  kind  of  direct  connection  with  outward  fact. 
In  the  end  it  may  actually  identify  itself  with  the  habitual 
feeling  which  we  have  of  ourselves.  And  this  common 
meeting-ground  of  illusion  and  truth  serves  often  to  confuse 
them  together  in  our  minds.  But  we  can  not  here  further 
pursue  these  discussions. 

§  37.  To  resume.  It  is  not  the  mere  symbolic  use  of  ideas 
which  distinguishes  truth  from  bare  imagination.  For  ima- 
gination is  not  confined  to  particular  images.  Tjust  as  in  per- 
ception it  is  hard  to  say  where  inference  first  appears,  and 
where  the  analytic  judgment  becomes  synthetic,  so  in  much 
imagination  we  shall  find  the  presence  of  a  discursive 
element.  The  idea  of  a  circle,  we  might  say  and  say  falsely, 
was  nothing  but  an  image ;  but  the  idea  of  a  chiliagon  would 
show  us  at  once  that  there  is  a  point  where  our  imagery  fails. 
And  it  is  obvious  that  ideas  of  abstract  relations  may  be  held 
before  the  mind  without  any  judgment.  This,  however,  is  a 
content  which  is  wholly  symbolic,  and  yet  (where  no  hypo- 
thetical judgment  comes  in)  it  is  purely  imaginary.  It  is 
detached  from  the  existence  of  the  image  in  our  minds,  but  it 
is  not  attached  to  another  reality. 

§  38.  We  now  perhaps  are  able  to  say  what  it  is  we  mean 
by  the  idea  of  an  individual  (or,  we  had  better  say,  of  a 
particular)  fact.  We  saw  the  futility  of  seeking  to  find  this  in 
the  proper  names  of  persons,  for  what  they  stand  for  is  never 
confined  to  a  single  event.  The  idea  of  par4;icularity  implies 
two  elements.  We  must  first  have  a  content  qualified  by 
"  thisness,"  and  we  must  add  to  that  content  the  general  idea 


Chap.  II.]  FORMS   OF  JUDGMENT.  ^^ 

of  reference  to  the  reality.  In  other  words  a  particular  must 
first  be  represented  in  a  series ;  this  gives  us  the  first  element. 
But  so  far  we  do  not  get  beyond  mere  "  thisness ; "  the 
members  are  exclusive,  within  the  series,  but  the  whole 
collection  is  not  unique.  To  get  the  complete  idea  of  a  par- 
ticular fact  we  must  make  our  series,  so  to  speak,  exter7ially 
exclusive  as  well  and  thus  particular.  And  we  do  not  do  this 
till  we  qualify  it  by  the  idea  of  reference  to  our  unique 
reality. 

If  we  actually  attributed  the  series  to  reality,  we  not  only 
should  have  got  the  idea  that  we  wanted,  but  also  more.  We 
should  have  judged  that  our  idea  was  true  in  fact.  And  in 
this  case  we  do  -not  wish  to  go  so  far.  We  desire  to  have  the 
idea  of  uniqueness,  but  not  to  assert  the  reality  of  the  idea. 

We  possess  as  we  have  seen  (§  24)  in  the  idea  of  "  this  "  the 
idea  of  immediate  contact  with  the  real,  and  it  is  this  idea 
we  must  add  to  our  series.  When  we  think  of  the  series  both 
as  a  whole,  and  as  touching  the  real  in  a  point  of  presentation, 
we  have  thought  of  it  then  as  truly  particular.  But  there 
we  must  stop.  For  if  we  went  on  to  judge  our  idea  to  be 
true,  we  should  have  to  find  it  a  special  place  in  the  unique 
series  which  extends  perception.  And  we  saw  that  to  use 
the  idea  of  "  this "  as  the  symbol  of  another  content  in 
judgment,  was  quite  impossible.  So  long,  however,  as  we 
abstain  from  judgment,  we  can  attach  the  aspect  of  "  this"  to 
a  content  other  than  that  which  is  really  presented. 

This  is  what  we  mean  by  the  idea  of  a  particular.  There 
is  a  difference  when  we  come  to  an  individual  person.  Our 
idea  is  there  particular,  since  it  has  limits  within  a  particular 
series.  But  it  also  involves  a  real  identity  persisting  through- 
out a  change  of  events.  And  so  it  falls  outside  the  class  of 
mere  synthetic  judgments. 

§  39.  Uniqueness  is  merely  the  negative  side  of  the  idea  of 
"this."  A  content  is  unique  when,  although  of  a  sort,  and  that 
means  regarded  from  the  aspect  of  content,  it  nevertheless  is  the 
same  as  no  other,  is  the  only  one  there  is  of  its  sort.  Unique- 
ness implies  the  idea  of  a  series,  -and  is  then  relative  or 
absolute.  It  is  relative  when  the  series,  which  contains  the 
element  which  excludes  the  others,  is  itself  7tot  unique.     In 


yZ  THE   PRINCIPLES  OF  LOGIC.  [Book  L 

any  universe  our  fancy  constructs  a  thing  may  be  unique, 
but  only  unique  within  that  universe.  We  have,  on  the  other 
hand,  absolute  uniqueness  when  the  series  is  connected  with 
direct  presentation.  In  that  case  the  relations  within  the 
series  fix  against  each  other  the  elements  it  holds,  and  no- 
thing can  be  fact  without  its  appearing  in  that  one  series.  But 
the  real  subject,  which,  in  predicating  uniqueness,  excludes 
any  other  event  of  the  kind,  we  must  remember,  is  not  the 
particular  event  as  such  and  taken  by  itself.  It  is  rather  the 
real  which  appears  in  that  particular  and  so  excludes  others. 
We  have  here  a  negative  existential  judgment,  for  the  nature 
of  which  we  must  consult  our  Third  Chapter. 

§  40.  After  meeting  many  difficulties,  some  of  which,  I 
trust,  may  have  been  overcome,  we  have  finished  our  account 
of  the  second  division  of  singular  judgments.  We  must 
pass  to  the  third,  the  assertions  not  confined  to  an  event  or 
a  number  of  events  in  time  (§  7).  But,  before  we  proceed, 
let  us  pause  for  a  moment,  and,  however  dangerous  the 
experiment  may  be,  let  us  try  to  put  before  our  very  eyes  a 
synthetic  judgment.  Let  us  call  before  our  mind  some 
series  of  pictures,  like  Hogarth's  Progress  of  the  harlot  or 
rake  ;  but  let  us  also  imagine  something  beside.  One  picture 
in  the  series  must  be  the  reality,  the  actual  person  in  a  real 
room,  and  on  the  walls  of  this  real  room  must  be  hung  the 
series  of  earlier  and  later  pictures.  By  virtue  of  the  sameness 
in  the  quality  of  the  man,  as  he  is  in  the  room  and  is  in  the 
pictures,  we,  neglecting  the  appearance  in  particular  frames, 
arrange  the  whole  series  as  his  past  and  future.  We  tran- 
scend in  this  way  the  visible  room  and  the  presented  scene, 
and  view  the  real  life  of  the  person  extending  itself  as  a  series 
in  time. 

But  the  man  in  the  real  room  that  we  see,  is  body  and 
bones  and  breath  and  blood,  while  his  past  and  future,  if  we 
mean  by  reality  a  sensible  fact,  are  nothing  in  the  world  but 
glass  and  wood  and  paint  and  canvas.  It  is  the  same  with 
all  our  future  and  past.  The  events  of  memory  and  of 
anticipation  are  facts  now  in  our  minds,  but  they  no  more  are 
the  reality  they  represent  than  paint  and  canvas  are  a 
throbbing  heart.     No  doubt  they  stand  for  reality,  and  we 


Chap.  II.]  FORMS   OF  JUDGMENT.  79 

flatter  ourselves  that,  if  they  can  not  be  fact,  at  least  they  are 
true.  True  indeed  they  may  be  if  truth  means  a  natural  and 
inevitable  way  of  representing  the  real.  But  if  by  their  truth 
we  understand  more  than  this ;  if  we  say  that  the  reality  is  as 
it  appears  in  our  ideal  construction,  and  that  actually  there 
exists  a  series  of  facts  past  present  and  future — I  am  afraid 
that  truth,  if  we  come  to  examine  it,  would  change  into 
falsehood.  It  would  be  false  if  measured  by  the  test  of 
perception,  and  it  may  be,  if  tried  by  another  standard,  would 
be  falser  still. 

§  41.  The  life  of  a  man  cannot  be  presented  in  any  one 
scene,  and  our  very  illustration  has  gone  farther  than  we 
thought.  That  life  is  not  even  a  mere  succession  of  serial 
events,  but  contains  (so  we  think  of  it)  a  something  the  same, 
a  real  identity  which  appears  in  all,  but  which  is  not  any,  nor 
even  every,  event.  We  find  ourselves  brought  to  the  third  main 
class  of  singular  judgments,  and  are  speaking  of  a  subject 
which  is  not  an  event.  These  judgments  are  separated  into 
two  divisions,  according  as  the  individual  with  which  they 
deal  is  related  to  some  given  period  of  time,  or  not  to  any 
time  in  particular. 

III.  (i)  In  the  history  of  a  man  or  nation  we  have  a 
content  referred  to  the  real,  but  to  the  real  as  it  appears 
throughout  one  certain  part  of  that  series  which  is  determined 
by  relation  to  given  perception,  (ii)  In  the  second  division 
we  must  place  any  judgments  we  make  about  the  Universe  or 
God  or  the  soul,  if  we  take  the  soul  to  be  eternal.  Our  ideas 
are  here  identified  with  the  real  that  we  find  in  perception, 
but  they  do  not  attach  themselves  to  any  one  part  of  the 
phenomenal  series.  It  may  be  said,  of  course,  that  such 
judgments  are  illusory.  But,  as  we  saw,  that  conclusion,  if 
true,  could  only  be  established  by  a  metaphysical  enquiry  we 
have  no  place  for.  The  judgments  exist,  and  logic  can  do 
nothing  else  but  recognize  them. 

This  third  and  last  class  of  singular  judgments  is  distinct 
from  the  others.  Its  essence  is  that  its  ultimate  subject  is 
not  the  real,  as  it  appears  in  the  "  this  "  or  in  any  one  event  in 
the  series.  But  the  distinction  is  to  a  certain  extent  unstable. 
Just   as   analytic  judgments  are  always  tending  to  become 


8o  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

synthetic,  so  here  it  is  impossible  to  separate  sharply  the  first 
division  of  this  class  from  synthetic  judgments.  On  the  one 
hand  the  continuity  of  the  element  of  time  strictly  excludes  a 
mere  serial  character.*  In  every  judgment  about  events  we 
unknowingly  are  asserting  the  existence  of  an  identity.  On 
the  other  hand  an  individual  living  in  a  series  seems  naturally 
to  belong  to  that  class  of  judgment  which  constructs  a  series. 
Since,  however,  when  an  individual  is  concerned,  we  explicitly 
recognize  something  real,  enduring  throughout  the  changes  of 
events,  it  is  better  perhaps  to  keep  up  a  distinction  which  in 
principle  must  be  admitted  to  fluctuate.  The  example  of  an 
individual  person  took  us  from  analytic  to  synthetic  judgments. 
And  it  has  served  again  to  carry  us  on  further. 

§  42.  We  have  now  considered  all  the  three  classes  of 
singular  judgments,  and  have  seen  in  what  way  they  attribute 
an  idea  to  the  real  which  appears.  We  have  already  anti- 
cipated the  account  to  be  given  of  Existential  judgments,  and 
may  deal  with  them  rapidly.  Confining  ourselves  here  to 
those  which  are  affirmative,  we  can  say  at  once  that  the 
subject  in  all  of  them  is  the  ultimate  reality,  either  {a)  as  it 
appears  in  some  part  of  the  series  determined  by  the  "  this," 
or  (b)  as  it  underlies  the  whole  series  of  phenomena.  When 
I  say  "  A  exists,"  or  "  A  is  real,"  the  content  A  is  in  truth  the 
predicate.  We  use  it  to  qualify  existence  or  reality,  in  one  of 
the  two  senses  we  have  now  mentioned. 

The  enquiry  into  existential  propositions  reduces  to 
absurdity  the  notion  that  judgment  consists  in  ideas.  If  we 
add  to  the  adjectival  idea  of  A  another  adjectival  idea  of 
reality,  then,  failing  wholly  in  reference  to  fact,  we  fall  entirely 
short  of  judgment.  But  this  is  not  all.  The  idea  of  reality, 
like  the  idea  of  "  this,"  is  not  an  ordinary  symbolic  content,  to 
be  used  without  any  regard  to  its  existence.  The  idea  of  what 
is  real,  or  of  that  which  exists,  is  found  as  an  element  in 
that  actual  reality  and  actual  existence  which  we  encounter 
directly.  It  can  not  in  judgment  be  removed  from  this,  and 
be  transplanted  away  to  another  reality.  We  have  here  the 
same  obstacle  which  met  us  before  (§§  25-27).  The  idea 
cannot  be  predicated  of  anything  except  its  own  reality.  For, 
to  get  the  idea,  you  must  take  it  by  a  distinction  from  what  is 


Chap.  II.]  FORMS   OF  JUDGMENT.  8 1 

given.  If  you  then  make  it  a  predicate  of  anything  not  given, 
you  have  a  collision,  and  your  judgment  disappears.  But 
if,  on  the  other  hand,  you  predicate  it  of  that  which  actually 
is  given,  your  procedure  is  idle.  Why  eniploy  an  idea  to 
assert  reality  when  you  have  the  fact,  and  when  your  ideal 
synthesis  is  a  mere  analysis  of  this  given  reality,  and 
attributed  in  the  end  to  that  as  subject?  "Real"  is  clearly 
the  adjective  of  "  reality,"  and  we  know  no  reality  but  what 
appears  in  presentation.  The  idea  then,  to  be  true,  must  be 
true  of  that  reality.  But,  if  so,  we  must  have  the  subject 
before  us  in  the  shape  of  fact,  and,  if  we  did  not,  the  idea 
would  at  once  become  false.  For  a  more  detailed  discussion 
we  may  refer  to  §§  25-27. 

Nor  would  it  repay  us  here  to  examine  the  somewhat 
surprising  view  which  Herbart  has  advocated  (vid.  §  75). 
Our  enquiries  in  this  chapter  should  have  prepared  us  for  the 
result  that  the  ultimate  subject  is  never  an  idea,  and  that 
the  idea  of  existence  is  never  a  true  predicate.  The  subject, 
in  the  end,  is  always  reality,  which  is  qualified  by  adjectives 
of  ideal  content. 

§  43.  We  cannot  say  there  is  a  class  of  existential  judg- 
ments, for  all  singular  judgments  have  by  this  time  been  shown 
to  be  existential.  And,  with  this  conclusion,  we  may  pass 
beyond  them  to  another  branch  of  affirmative  judgments.  In 
these  we  no  longer  have  to  do  with  any  particular  facts  nor 
in  any  sense  with  separate  individuals.  They  are  universal  in 
the  sense  of  transcending  what  is  singular.  They  are  not 
"  concrete "  but  "  abstract,"  since,  leaving  things,  they  assert 
about  qualities,  alone  or  in  synthesis.  In  ihis  respect,  we 
may  remark  in  passing,  there  is  no  real  difference  between  the 
"general"  and  the  "abstract:"  for,  taken  in  comparison 
with  the  particular  thing,  the  general  idea  is  a  mere  abstrac- 
tion. 


§  44.  We  have  reached  the  common  type  of  universal 
judgment ;  and  the  point  in  this  which  we  notice  at. once,  is 
that  every  such  judgment  is  concerned  with  adjectivals.  They 
assert  a  connection  between  elements  of  content,  and  say 
nothing  about  the  place  of  those  elements  in  the  series  of 

G 


82  THE   PRINCIPLES  OF  LOGIC.  [Book  L 

events.  In  "  Equilateral  triangles  are  equiangular  "  all  I  affirm 
is  that  with  one  set  of  qualities  you  will  have  the  other  set, 
but  I  make  no  assertion  about  where  and  when.  And 
"  Mammals  are  warm-blooded  "  does  not  tell  me  anything 
about  this  or  that  mammal.  It  merely  assures  me  that, 
finding  one  attribute,  I  shall  find  the  other. 

The  fact  that  is  asserted  in  an  abstract  judgment  is  not 
the  existence  of  the  subject  or  predicate  (§  6),  but  simply  the 
connection  between  the  two.  And  this  connection  rests  on  a 
supposal.  The  abstract  universal,  "  A  is  B,"  means  no  more 
than  "  given  A,  in  that  case  B,"  or  "  if  A,  then  B."  In  short, 
such  judgments  are  always  hypothetical  and  can  never  be 
categorical.  And  the  proper  terms  by  which  to  introduce 
them  are  "given,"  or  "if,"  or  "whenever,"  or  "where,"  or 
"  any,"  or  "  whatever."     We  should  beware  of  "  all."' 

§  45.  For  the  use  of  "all,"  we  have  seen  above  (§  6),  is 
most  misleading  and  dangerous.  It  encourages  that  tendency 
to  understand  the  universal  in  the  sense  of  a  collection,  which 
has  led  to  so  many  mistaken  consequences.  ]  We  shall  glance 
elsewhere  at  that  extraordinary  teaching  on  the  subject  of 
quantity,  in  which  the  traditional  logic  delights.  And  we 
shall  see  hereafter,  when  we  come  to  inference,  the  absurd 
incompetence  of  the  dictum  de  omni.  \  For  our  present  purpose 
we  need  criticize  no  further  the  attempt  to  understand  the 
"  all  "  collectively.  Even  if  that  use  were  justifiable  in  itself, 
it  would  here  be  irrelevant ;  for  a  judgment  where  "  all " 
means  a  real  collection  of  actual  cases,  belongs  to  a  class  we 
have  already  disposed  of  If  "all"  signifies  a  number  of 
individual  facts,  the  judgment  is  concerned  with  actual 
particulars.  And  so  it  obviously  is  but  one  form  of  the 
singular  judgment.  "All  A  is  B,"  will  be  an  abbreviated 
method  of  setting  forth  that  this  A  is  B,  and^  that  A  is  B, 
and  the  other  A  is  B,  and  so  on  until  the  lot  is  exhausted. 
Such  judgments  fall  clearly  under  the  head  of  singular. 

But,  when  this  class  is  banished  to  the  preceding  category, 
have  we  any  universal  judgments  left  us  ?  We  can  not  doubt 
that ;  for  there  are  judgments  which  do  not  assert  the  existence 
of  particular  cases.  We  come  at  once  upon  the  judgments 
that  connect  adjectival  elements,  and  that  say  nothing  about 


Chap.  II.]  FORMS  OF  JUDGMENT.  83 

the   series   of  phenomena.     These    abstract    universals    are 
always  hypothetical  and  never  categorical.* 

§  46.  At  this  point  we  must  pause  to  encounter  an 
objection.  "The  distinction,"  we  may  be  told,  "between 
categorical  and  hypothetical  is  really  illusory.  Hypothetical 
judgments  can  all  be  reduced  to,  and  in  the  end  are  nothing 
but,  a  kind  of  categorical."  If  this  were  well  founded,  it 
would  certainly  occasion  us  serious  difficulty.  But  I  do  not 
think  we  need  much  disturb  ourselves. 

/*'  If  A  is  B  it  is  C,"  we  may  be  told,  "is  equivalent  to  The 
instances  or  cases  of  A  that  are  B  are  also  C,  and  this  is 
surely  a  categorical  judgment."  I  answer,  if  "  the  cases  of  A 
that  are  B  "  means  the  existing  cases  of  A  B,  and  no  others, 
then  the  judgment  no  doubt  is  categorical,  but  it  is  not  an 
abstract  universal.  It  is  merely  collective,  and  it  most  cer- 
tainly does  not  mean  what  we  meant  by  our  hypothetical 
judgment.  "If  butter  is  held  to  the  fire  it  melts"  is  no 
assertion  about  mere  existing  pats  of  butter.  )And  when  it  is 
reduced  to  the  form,  "  All  cases  of  the  holding^  of  butter,  &c.," 
it  does  not  become  any  more  categorical.  "  All  cases " 
means  here  "  Suppose  any  case." 

Indeed,  if  we  steadily  keep  in  view  the  difference  between 
a  simple  assertion  about  fact  and  an  assertion  on  the  strength 
of  and  about  a  supposition,  we  may  perhaps  be  puzzled,  but 
we  are  not  likely  to  be  led  far  astray  by  these  elementary 
mistakes. 

§  47.  And  with  this  remark  I  could  leave  the  matter. 
But  it  is  perhaps  worth  while,  by  another  instance,  to  illustrate 
the  futility  of  this  attempt  to  turn  hypothetical  into  categorical 
judgments,  J.  S.  Mill  in  his  Logic  (I.  4,  §  3)  approaches  the 
subject  with  an  air  of  easy  superiority.  "A  conditional  pro- 
position is  a  proposition  concerning  a  proposition." 

"  What  is  asserted  is  not  the  truth  of  either  of  the  proposi- 
tions but  the  inferribility  of  the  one  from  the  other."  "  If  A  is 
B,  C  is  D  is  found  to  be  an  abbreviation  of  the  following  : 

*  The  extensional  theory  of  judgment  and  reasoning  is  dealt  with  else- 
where (Chap.  VI.  and  Book  II.  Part  1 1. Chap.  IV.).  We  may  here  remark 
that,  taking  "  A  is  B  "  to  mean  "  the  things  that  are  A  are  the  things  that  are 
B,"  the  judgment  must  be  singular,  if  an  existing  set  of  things  be  denoted, 
and  will  be  universal  and  abstract  if  possible  things  are  included  as  well. 

G   2 


84  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

'The  proposition  C  is  D,  is  a  legitimate  inference  from  the 
proposition  A  is  B.'  " 

How  this  doctrine  is  connected  with  Mill's  other  views  as 
to  the  import  of  propositions,  an  expert  in  Mill-philology  no 
doubt  could  inform  us.  But,  left  to  ourselves,  we  can  only 
conjecture  the  doctrine  he  here  intended  to  teach.  (i)  If  he 
really  meant  "  inferribility"  then  cadit  qucestio.  For  at  once 
the  statement  is  not  about  what  is,  but  what  may  be  or  might 
be.  It  is  not  simply  about  existing  propositions,  but  clearly 
involves  a  supposal  of  some  kind,  and  is  therefore  not  reduced 
to  categorical  form.  It  is  still  Suppose  you  have  got  AB,  then 
you  may  go  legitimately  to  CD.  (ii)  But  no  doubt  there  is 
more  than  this  verbal  quibble.  He  tells  us  that  one  is  an 
inference  from  the  other.  Does  this  mean  (oi)  that  both  are 
actually  asserted,  and  that  I  further  assert  that  I  really  have 
argued  to  the  second  from  the  first  ?  Surely  not  that :  but  then 
what  else  }  {b)  Can  it  mean  that,  without  asserting  either 
proposition,  I  hold  them  in  my  mind,  and  affirm  their  con- 
nection }  It  may  mean  this.  But  then  this  process  of  taking 
up  a  statement  without  believing  it,  and  of  developing  its 
consequences,  is  in  fact  nothing  else  than  a  supposition.  The 
connection  asserted  is  not  between  realities,  and  the  pro- 
position is  still  hypothetical.  (iii)  But  the  extraordinary 
illustrations  towards  the  end  of  the  section  point  to  another 
interpretation  ;  "  The  subject  and  predicate  are  names  of 
propositions."  Without,  however,  attempting  the  hopeless 
task  of  understanding,  we  may  perhaps  state  the  issue  in  the 
form  of  a  dilemma.  Either  (a)  one  proposition,  in  the  sense 
of  a  little  heap  of  words,  does,  as  a  particular  event  in  my 
head,  now  follow  another  such  heap  ;  or  {b)  it  would  follow,  if 
the  other  were  there.  The  second  alternative  is  of  course  still 
hypothetical.  In  the  former  at  last  we  have  got  to  something 
categorical,  but  nothing  to  which  a  hypothetical  judgment 
(or  indeed  any  judgment)  could  possibly  be'  reduced.  It 
would  be  an  error  too  gross  to  merit  refutation. 

Whatever  else  may  be  the jneaning  of  the  writer,  we  after 
all  mayTemain  sure  of  this.  -^  Either  the  categorical  judgment, 
to  which  he  professes  to  redlice  the  hypothetical,  is  not  its 
equivalent ;    or  else  it  contains,    under   some   flimsy   veil    of 


Chap.  II.]  FORMS   OF  JUDGMENT.  85 

verbal  ambiguity,  a  supposition  which  is  the  condition  of  the 
judgment. 

§  48.  Such  universal  judgments  are  all  hypothetical,  and 
with  this  conclusion  we  are  landed  once  more  in  our  former 
difficulties  (§  6).  Judgment,  we  saw,  always  meant  to  be  true, 
and  truth  must  mean  to  be  true  of  fact.  But  here  we  en- 
counter judgments  which  seem  not  to  be  about  fact.  For  a 
hypothetical  judgment  must  deal  with  a  supposal.  It  appears 
to  assert  a  necessary  connection,  which  holds  between  ideas 
within  my  head  but  not  outside  it.  But,  if  so,  it  can  not  be  a 
judgment  at  all ;  while  on  the  other  hand  it  plainly  does 
assert  and  can  be  true  or  false. 

We  are  not  able  to  rest  in  this  conclusion,  and  yet  we  can 
not  take  back  our  premises.  Let  us  then  try  to  look  more 
closely  at  the  problem,  and  ask  more  narrowly  what  is  involved 
in  these  judgments.  And,  in  the  first  place,  we  can  not  expect 
to  succeed  until  we  know  what  a  supposal  is. 

A  supposition,  in  the  first  place,  is  known  to  be  ideal,  and 
known  perhaps  to  diverge  from  fact.  At  a  low  stage  of  mind, 
where  everything  is  fact  (cf.  Chap.  I.),  it  could  not  exist.  For 
the  supposed  must  be  known  as  an  ideal  content,  and,  in 
addition,  it  has  to  be  retained  before  the  mind  without  a 
judgment.  It  is  not  referred  as  an  adjective,  either  posi- 
tively or  negatively,  to  the  real.  In  other  words  reality  is  not 
qualified  either  by  the  attribution  or  the  exclusion  of  it.  But 
though  it  does  not  judge,  a  supposition  is  intellectual,  for  (as 
such),  it  excludes  desire  and  emotion.  And  again  it  is  more 
than  mere  imagination,  for  it  is  fixed  by  attention  and  pre- 
serves, or  should  preserve,  its  identity  of  content  (vid.  Book  III. 
Chap.  III.  §§  23,  24).  It  certainly  is  all  this,  and  yet  this  is 
not  all.  For  to  think  of  a  chimaera  is  not  quite  the  same  thing 
as  to  siLppose  a  chimaera. 

A  supposition  means  thinking  for  a  particular  end,  and  in 
a  special  way.  It  is  not  a  mere  attending  to  a  certain  meaning, 
or  an  analysis  of  its  elements.  It  has  a  reference  to  the  real 
world,  and  it  involves  a  desire  to  see  what  happens.  We  may 
illustrate  perhaps  from  other  usages.  "  Say  it  is  so  for  argu- 
ment's sake,"  "Treat  it  as  this  and  then  you  will  see,"  are 
much  the  same  as,   "  Suppose  it  to  be  so."      A  supposal  is,  in 


S6  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

short,  an  ideal  experiment.  It  is  the  application  of  a  content 
to  the  real,  with  a  view  to  see  what  the  consequence  is,  and 
with  a  tacit  reservation  that  no  actual  judgment  has  taken 
place.  The  supposed  is  treated  as  if  it  were  real,  in  order  to  see 
how  the  real  behaves  when  qualified  thus  in  a  certain  manner. 
\  You  might  say  it  is  the  adding  the  idea  of  existence  to  a 
givien  thought,  while  you  abstain  from  judgment.  But  that  I 
do  not  think  would  be  satisfactory.  For  it  is  not  the  mere  idea  of 
existence  that  is  used.  What  we  use  is  the  real  that  is  always 
in  immediate  contact  with  our  minds,  and  which  in  a  variety 
of  judgments  we  already  have  qualified  by  a  certain  content. 
And  it  is  to  this  that  we  bring  up  another  idea,  in  order  to  see 
what  result  will  come  of  it. 

§  49.  So  far  there  is  neither  truth  nor  falsehood,  for  we 
have  not  judged.  The  operation,  we  may  say,  is  so  far 
"subjective."  It  is  all  our  own  doing,  and  all  of  it  holds 
inside  our  heads,  and  not  at  all  outside.  The  real  is  not 
qualified  by  the  attribute  we  apply  to  it.  But,  so  soon  as  we 
judge,  we  have  truth  or  falsehood,  and  the  real  is  at  once 
concerned  in  the  matter.  The  connection  of  the  consequence, 
of  the  "  then  "  with  the  "  if,"  of  the  result  of  our  experiment 
with  its  conditions,  is  the  fact  that  is  asserted,  and  that  is  true 
or  false  of  the  reality  itself 

But  the  question  is  kow.  You  do  not  assert  the  existence 
of  the  ideal  content  you  suppose,  and  you  do  not  assert  the 
existence  of  the  consequence.  And  you  can  not  assert  the 
existence  of  the  connection,  for  how  can  a  connection  remain 
as  a  fact  when  no  facts  are  connected  ?  "  If  you  only  had 
been  silent  you  would  have  passed  for  a  philosopher."  But 
you  were  not  silent,  you  were  not  thought  a  philosopher,  and 
one  was  not,  and  could  not  possibly  de,  a  result  of  the  other. 
If  the  real  must  be  qualified  by  the  connection  of  the  two,  it 
seems  that  it  will  not  be  qualified  at  all.  Neither  condition, 
nor  result,  nor  relation  can  be  ascribed  to  it :  and  yet  we  musf 
ascribe  something,  for  we  judge.     But  what  can  it  be  ? 

§  50.  When  I  go  to  a  man  with  a  fictitious  case,  and  lay 
before  him  a  question  of  conduct,  and  when  he  replies  to  me, 
"  I  should  act  in  this  way,  and  not  in  the  other  way,"  I  may 
come  from  him  with  some  knowledge  of  fact.     But  the  fact  is 


Chap.  II.J  FORMS  OF  JUDGMENT.  8/ 

not  the  invented  position,  nor  yet  the  hypothetical  course  of 
action,  nor  the  imaginary  relation  between  the  two.  The  fact 
is  the  quality  in  the  man's  disposition.  It  has  answered  to  a 
trial  in  a  certain  way.  But  the  test  was  a  fiction,  and  the 
answer  is  no  fact,  and  the  man  is  not  qualified  by  one  or  the 
other.  It  is  his  latent  character  that  is  disclosed  by  the 
experiment. 

It  is  so  with  all  hypothetical  judgment.  The  fact  that  is 
affirmed  as  an  adjective  of  the  real,  and  on  which  depends  the 
truth  or  falsehood,  does  not  explicitly  appear  in  the  judgment. 
Neither  conditions  nor  result  of  the  ideal  experiment  are  taken 
to  be  true.  What  is  affirmed  is  the  mere  ground  of  the  con- 
nection ;  not  the  actual  existing  behaviour  of  the  real,  but  a 
latent  quality  of  its  disposition,  a  quality  which  has  appeared 
in  the  experiment,  but  the  existence  of  which  does  not  depend 
on  that  experiment.  "  If  you  had  not  destroyed  our  barometer, 
it  would  now  forewarn  us."  In  this  judgment  we  assert  the 
existence  in  reality  of  such  circumstances,  and  such  a  general 
law  of  nature,  as  would,  if  we  suppose  some  conditions  present, 
produce  a  certain  result.  But  assuredly  those  conditions  and 
their  result  are  not  predicated,  nor  do  we  even  hint  that  they 
are  real.  They  themselves  and  their  connection  are  both 
impossible.  It  is  the  diminution  of  pressure  and  the  law  of 
its  effect,  which  we  affirm  of  the  actual  world  before  us.  And 
of  course  that  law  is  resolvable  further  (§  52). 

§  51.  In  all  judgment  the  truth  seems  none  of  our  making. 
We  perhaps  need  not  judge,  but,  if  we  judge,  we  lose  all  our 
liberty.  In  our  relation  to  the  real  we  feel  under  compulsion 
(§  4).  In  a  categoric  judgment  the  elements  themselves  are 
not  dependent  on  our  choice.  Whatever  we  may  think  or  say, 
they  exist.  But,  in  a  hypothetic  judgment,  there  is  no  com- 
pulsion as  regards  the  elements.  The  second,  indeed,  depends 
on  the  first,  but  the  first  is  arbitrary.  It  depends  on  my 
choice.  I  may  apply  it  to  the  real,  or  not,  as  I  please  ;  and  I 
am  free  to  withdraw  the  application  I  have  made.  And,  when 
the  condition  goes,  the  result  goes  too.  The  compulsion 
extends  no  further  than  the  connection,  and  yet  it  does  not 
even  extend  to  the  connection  as  such.  The  relation  of  the 
elements  in  a  hypothetical  judgment  is  not  an  actual  attribute 


88  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

of  the  real,  for  that  relation  itself  is  arbitrary.  It  need  not  be 
true  outside  the  experiment.  The  fact  which  existed  before 
the  experiment,  and  remains  true  after  it,  and  in  no  way- 
depends  on  it,  is  neither  the  elements,  nor  the  relation  between 
them,  but  it  is  a  quality.  It  is  the  ground  of  the  sequence 
that  is  true  of  the  real,  and  it  is  this  ground  which  exerts 
compulsion. 

§  52.  This  quality  of  the  real  is  not  explicit  in  the  judg- 
ment, and,  in  respect  of  that  judgment,  is  occult  or  latent. 
We  know  it  is  there  because  of  its  effects,  but  we  are  not  able 
to  say  what  it  is.  We  can  not  even  tell,  without  further  enquiry, 
that  it  is  not  the  same  as  what  we  have  asserted  in  another 
judgment,  the  elements  of  which,  and  also  their  relation,  were 
very  different  (cf.  Chap.  III.  §  19).  And,  when  we  push  the 
investigation  further,  and  ask.  Are  these  qualities,  that  thus 
seem  to  lie  at  the  base  of  our  judgments,  altogether  latent,  or 
only  latent  each  in  respect  of  its  peculiar  judgment,  then  we 
get  at  once  into  difficult  questions.  It  is  certain  on  the  one 
hand  that  we  can  find  the  grounds  of  many  such  judgments, 
which  thus  have  relatively  become  explicit.  But  this  only 
serves  to  bring  us  nearer  to  the  doubt,  whether  in  the  end  they 
have  ceased  to  be  latent.  Do  we  ever  get  to  a  ground  of 
judgment  which  we  can  truly  ascribe  to  the  real  as  its  quality  ? 
Or  are  we  left  with  ultimate  judgments,  which  are  certainly 
true,  but  neither  the  elements  nor  relations  of  which  are  true 
of  reality  ?  Must  we  say,  in  the  end,  that  the  quality,  which 
we  know  is  the  base  of  our  synthesis,  remains  in  other  ways 
altogether  unknown  and  is  finally  occult  ?  We  seem  here  to 
be  asking,  in  another  form,  for  the  limits  of  explanation,  and  it 
would  be  the  task  of  metaphysics  to  pursue  an  enquiry  which 
must  here  be  broken  off. 

§  53.  We  have  seen  that,  what  hypothetical  judgments 
assert,  is  simply  the  quality  which  is  the  ground  of  the 
consequence.  And  all  abstract  universals,  we  have  seen,  are 
hypothetical.  It  may  here  be  asked  Are  the  two  things 
one  }     Are  all  hypothetical  judgments  thus  universal } 

This  might  for  a  moment  appear  to  be  doubtful,  since  the 
real,  to  which  application  is  made,  is  at  times  an  individual. 
And  for  the  purposes  of  this,  and  the  following  section,  I  will 


Chap.  II.]  FORMS   OF  JUDGMENT.  89 

give  some  examples  ;  "  If  God  is  just  the  wicked  will  be 
punished,"  "  Had  I  a  toothache  I  should  be  wretched,"  "  If 
there  were  a  candle  in  this  room  it  would  be  light,"  "  If  it  is 
now  six  o'clock  we  shall  have  dinner  in  an  hour,"  "  If  this 
man  has  taken  that  dose,  he  will  be  dead  in  twenty  minutes." 
It  may  surprise  some  readers  to  hear  that  these  judgments  are 
as  universal  as  "  All  men  are  mortal : "  but  I  think  we  shall 
find  that  such  is  the  case. 

In  the  first  place  it  is  certain  that  in  none  of  these  judg- 
ments is  the  subject  taken  to  be  actually  real.  We  do  not 
say  above  that  a  just  God  exists,  or  that  I  have  a  toothache ; 
we  only  suppose  it.  The  subject  is  supposed,  and,  if  we 
consider  further,  we  shall  find  that  subject  is  nothing  more 
than  an  ideal  content,  and  that  what  is  asserted  is  not 
anything  beside  a  connection  of  adjectives.  The  "  that,"  the 
"this,"  the  "I,"  the  "now,"  do  not  really  pass  into  the 
supposition.  They  are  the  point  of  reality  to  which  we  apply 
our  ideal  experiment,  but  they  themselves  are  in  no  case 
supposed.  More  or  less  of  their  content  is  used  in  the 
hypothesis,  and  passes  into  the  subject.  But,  apart  from 
themselves,  their  content  can  not  possibly  be  called  individual. 

§  54.  This  would  hardly  be  doubtful,  were  it  not  for  the 
ambiguity  of  all  these  assertions,  a  point  to  which  we  should 
carefully  attend.  "  If  he  had  murdered  he  would  have  been 
hanged,"  may  perhaps  assert  nothing  but  the  general  con- 
nection of  hanging  with  murder,  and  the  "  he  "  is  irrelevant. 
But  "  if  God  is  just  the  wicked  will  be  punished,"  may  perhaps 
not  say  that  punishment  would  follow  from  aiiy  justice,  but 
only  from  justice  that  is  qualified  by  omnipotence.  On  the 
other  hand,  when  you  say  "  If  this  man  has  taken  that  dose, 
&c,,"  you  do  not  tell  me  if  his  speedy  death  would  happen 
because  the  dose  would  poison  any  one,  or  would  only  poison 
such  a  man  as  he  is,  or  would  not  even  poison  such  a  kind  of 
man,  unless  under  present  special  conditions.  And  the  other 
examples  would  all  entangle  us  in  similar  ambiguities.  The 
supposition  is  not  made  evident,  and  reflection  convinces  us 
that,  supposing  we  know  the  subject  of  the  judgment,  at  all 
events  we  do  not  display  our  knowledge. 

§  55.  And  since  this  is  so,  since  the  adjectival  content  is  not 


90  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

made  explicit,  since  all  we  have  is  an  indefinite  reference  to 
this  or  that  case,  we  fall  into  the  mistake  of  thinking  it  is  the 
particular  we  have  to  deal  with.  But  our  real  assertion,  when 
we  come  to  analyze  it,  never  takes  in  the  "  that,"  or  the  "  now," 
or  the  "  this."  It  is  always  the  content  about  which  we  assert. 
But,  because  we  are  not  clear  what  that  content  is,  and 
because  we  know  it  is  to  be  found  in  the  individual  as 
supposed,  we  fire,  so  to  speak,  a  charge  of  shot  instead  of  a 
bullet,  and  take  the  individual  as  the  point  of  reality  to  which 
our  supposition  is  to  be  confined.  In  this  way  we  give  rise 
to  the  erroneous  idea  that  the  reality  itself  passes  into  the 
supposal.  The  fact,  as  we  have  seen,  is  that  some  of  the 
content  either  is  or  makes  part  of  the  adjectival  condition 
about  which  we  assert.  But,  because  that  content  has  not 
been  analyzed,  we  go  to  the  individual  to  get  it  in  the  lump. 
The  real  judgment  is  concerned  with  nothing  but  the 
individual's  qualities^  and  asserts  no  more  than  a  connection 
of  adjectives.  In  every  case  it  is  strictly  universal  as  well  as 
hypothetical. 

/  §  56.  We  have  found,  thus  far,  that  all  abstract  judgments 
are  hypothetical,  and  in  this  connection  we  have  endeavoured 
to  show  what  a  supposition  is,  and  to  lay  bare  that  occult 
affirmation  as  to  the  real,  which  is  made  in  every  hypothetical 
judgment.  Singular  judgments  we  have  already  discussed, 
and  we  found  that,  be  they  analytic  or  synthetic,  they  all  at 
first  sight  seem  categorical.  They  do  not  merely  attribute 
to  the  real  a  latent  quality,  which  manifests  itself  in  an  unreal 
relation,  but  they  qualify  the  real  by  the  actual  content  which 
appears  in  the  judgment.  It  is  not  the  mere  connection,  but 
the  very  elements  which  they  declare  to  exist. 

We  have  still  remaining  another  kind  of  judgment  (§  7),  but, 
before  we  proceed,  it  is  better  to  consider  the  result  we  have 
arrived  at.  That  result  perhaps  may  call  for  revision,  and  it 
is  possible  that  the  claim  of  the  singular  judgment  to  a 
categoric  position  may  not  maintain  itself. 


Chap.  IL]  FORMS   OF  JUDGMENT.  9I 


CHAPTER  IL  {Continued). 

§  57.  What  is  the  position  in  which  we  now  find  our- 
selves ?  We  began  with  the  presumption  that  a  judgment, 
if  true,  must  be  true  of  reality.  On  the  other  hand  we  found 
that  every  abstract  universal  judgment  was  but  hypothetical. 
We  have  endeavoured  to  reconcile  these  conflicting  views  by 
showing  in  what  way,  and  to  what  extent,  a  conditional 
judgment  asserts  of  the  fact.  But  singular  judgments  stand 
apart,  and  have  claimed  to  be  wholly  categorical,  and  true  of 
the  reality ;  and  hence  they  demand  a  position  above  that 
given  to  universal  judgments.  We  must  now  scrutinize 
this  pretension.  We  must  still  defer  all  notice  of  those 
individual  judgments  which  transcend  the  series  of  events  in 
time.  Confining  ourselves  to  judgments  about  the  pheno- 
menal series,  let  us  proceed  to  ask.  Are  they  categorical  .'*  Do 
they  truly  and  indeed  rank  higher,  and  closer  to  the  real 
world,  than  those  universal  judgments  which  we  found  were 
hypothetical?  We  shall  pefhaps  do  well  to  prepare  our 
minds  for  an  unwelcome  conclusion. 

In  passing  from  the  singular  to  the  universal  judgment,  we 
seem  to  have  been  passing  away  from  reality.  Instead  of  a 
series  of  actual  phenomena  connected  with  the  point  of 
present  perception,  we  have  but  a  junction  of  mere  adjectivals, 
the  existence  of  which  we  do  not  venture  to  affirm.  In  the 
one  case  we  have  what  seem  solid  facts  :  in  the  other  we  have 
nothing  but  a  latent  quality,  the  mere  name  of  which  makes 
us  feel  uneasy.  We  have  not  quite  lost  our  hold  of  the  real, 
but  we  seem  to  have  left  it  a  long  way  off.  We  keep  our 
connection  by  an  impalpable  thread  with  a  veiled  and  some- 
what ambiguous  object. 

But  our  thoughts  may  perhaps  take  a  difi*erent  colour,  if  we 
look  around  us  in  the  region  we  have  come  to.  However 
strange  it  may  seem  to  us  at  first,  yet  our  journey  towards 


92  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

shadows  and  away  from  the  facts  has  brought  us  at  last  to 
the  world  of  science.  The  end  of  science,  we  all  have  been 
taught,  is  the  discovery  of  laws  ;  and  a  law  is  nothing  but  a 
hypothetical  judgment.  It  is  a  proposition  which  asserts  a 
synthesis  of  adjectivals.  It  is  universal  and  abstract.  And  it 
does  not  assert  the  existence  of  either  of  the  elements  it 
connects.  It  may.  imply  this  (§  6),  but  such  an  implication  is 
not  essential.  In  mathematics,  for  instance,  the  truth  of  our 
statement  is  absolutely  independent  of  the  existence  of  either 
subject  or  predicate.  In  physics  or  chemistry  the  truth  does 
not  depend  on  the  actual  existence  at  the  present  moment  of 
the  elements  and  their  relation.  If  it  did  so,  the  law  might  be 
true  at  one  instant  and  false  at  the  next.  When  the  physio- 
logist, again,  tells  that  strychnine  has  a  certain  effect  on 
nerve-centres,  he  does  not  wait  to  enunciate  his  law  until  he 
is  sure  that  some  dose  of  strychnine  is  operating  in  the  world  : 
nor  does  he  hasten  to  recall  it  as  soon  as  he  has  lost  that 
assurance.  It  would  be  no  advantage  to  dwell  upon  this 
point.  It  may  be  regarded  now  as  a  certain  result,  that  the 
strict  expression  for  all  universal  laws  must  begin  with  an 
"if,"  and  go  on  with  a  "  then." 

§  58.  And  from  this  we  may  draw  a  certain  presumption. 
If  the  singular  judgment  is  nearer  the  fact,  and  if,  in  leaving 
it,  we  have  actually  receded  from  reality,  yet  at  least  in  science 
that  is  not  felt  to  be  the  case.  And  there  is  another  presump- 
tion which  may  help  to  strengthen  us.  In  common  life  we  all 
experience  the  tendency  to  pass  from  one  single  case  to  some 
other  instance.  We  take  what  is  true  at  one  time  and  place 
to  be  always  true  at  all  times  and  places.  We  generalize  from 
a  single  example.  We  may  deplore  this  tendency  as  an 
ineradicable  vice  of  the  unphilosophic  mind,  or  we  may 
recognize  it  as  the  inevitable  condition  of  all  experience,  and 
the  sine  qua  non  of  every  possible  inference  (vid.  Book  II.). 
But  in  either  case,  let  us  recognize  it  or  deplore  it,  we  still  do 
not  feel  the  passage  we  have  made  as  an  attempt  to  go  from 
the  stronger  to  the  weaker,  from  that  which  is  more  true  to 
that  which  is  less.  And  yet,  without  doubt,  it  is  a  transition 
away  from  the  individual  to  the  universal  and  hypothetical. 

§  59.  But  a  matter  of  this  sort  is  not  settled  by  presump- 


Chap.  IL]  FORMS   OF  JUDGMENT.  93 

tions.  There  are  prejudices,  it  may  be,  that  operate  both 
ways.  And  we  may  be  told,  on  behalf  of .  the  singular 
judgment,  that  it  is  the  fact  that  these  judgments  are 
categorical  ;  for  they  do  assert  the  actual  existence  of  their 
adjectival  content  :  and,  attributing  to  the  real  an  explicit 
quality,  they  are  truer  than  any  hypothetical  judgment,  if 
indeed  they  are  not  the  only  true  judgments.  Such,  we  take 
it,  is  the  claim  of  the  singular  judgment,  and  it  can  not  be 
denied  that  its  claim  in  one  respect  is  very  well  founded.  It 
does  assert  the  existence  of  its  content,  and  does  affirm 
'  directly  of  the  real.  But  the  answer  we  must  make  is  that, 
although  it  does  so  assert  and  affirm,  yet,  when  we  leave  the 
popular  view  and  look  more  closely  at  the  truth  of  things,  the 
assertion  and  affirmation  which  it  makes  are  false^  and  the 
claim  it  puts  forward  rests  on  a  mistake.  We  must  subject 
the  pretensions  of  the  singular  judgment  to  an  examination 
which  we  think  may  prove  fatal. 

§  60.  We  need  spend  no  time  on  the  synthetic  judgment. 
In  transcending  what  is  given  by  actual  perception,  we 
without  any  doubt  make  use  of  an  inference.  A  synthesis  of 
adjectives  is  connected  with  the  present  by  virtue  of  the 
identity  of  a  point  of  content.  By  itself  this  synthesis  is 
_  merely  universal,  and  is  therefore  hypothetical.  It  becomes 
categoric  solely  by  relation  to  that  which  is  given,  and  hence 
the  whole  weight  of  the  assertion  rests  on  the  analytic  judg- 
ment. If  that  is  saved,  it  will  then  be  time  to  discuss  its 
extension :  but  if,  on  the  other  hand,  the  analytic  be  lost,  it 
carries  with  it  the  synthetic  judgment. 

§  61.  Let  us  turn  at  once  to  the  judgments  which  assert 
within  what  is  given  in  present  perception.  These  seem 
categorical  because  they  content  themselves  with  the  analysis 
of  the  given,  and  predicate  of  the  real  nothing  but  a  content 
that  is  directly  presented.  And  hence  it  appears  that  the 
elements  of  these  judgments  must  actually  exist.  An  ideal 
content  is  attributed  to  the  real,  which  that  very  real  does 
now  present  to  me.  I  am  sure  that  nothing  else  is  attributed. 
I  am  sure  that  I  do  not  make  any  inference,  and  that  I  do  not 
generalize.  And  how  then  can  my  assertion  fail  to  be  true } 
How,  if  true,  can  it  fail  to  be  categorical  ? 


94  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

We  maintain,  on  the  other  hand,  that  analytic  judgments 
of  sense  are  all  false.  There  are  more  ways  than  one  of  saying 
the  thing  that  is  not  true.  It  is  not  always  necessary  to  go 
beyond  the  factS-_  It  is  often  more  than  enough  to  come 
short  of  them.^i  And  it  is  precisely  this  coming  short  of  the 
fact,  and  stating  a  part  as  if  it  were  the  whole,  which  makes 
the  falseness  of  the  analytic  judgment.  \ 

§  62.  The  fact,  which  is  given  us,Ts  the  total  complex  of 
qualities  and  relations  which  appear  to  sense»  But  what  we 
assert  of  this  given  fact  is,  and  can  be,  nothing  but  an  ideal 
content.  And  it  is  evident  at  once  that  the  idea  we  use  can 
not  possibly  exhaust  the  full  particulars  of  what  we  have 
before  us.  A  description,  we  all  know,  can  not  ever  reach  to 
a  complete  account  of  the  manifold  shades,  and  the  sensuous 
wealth  of  one  entire  moment  of  direct  presentation.  As  soon 
as  we  judge,  we  are  forced  to  analyze,  and  forced  to  dis- 
tinguish. We  must  separate  some  elements  of  the  given  from 
others.  We  sunder  and  divide  what  appears  to  us  as  a 
sensible  whole.  It  is  never  more  than  an  arbitrary  selection 
which  goes  into  the  judgment.  We  say  "  There  is  a  wolf,"  or 
"  This  tree  is  green  : "  but  such  poor  abstractions,  such  mere 
bare  meanings,  are  much  less  than  the  wolf  and  the  tree  which 
we  see  ;  and  they  fall  even  more  short  of  the  full  particulars, 
the  mass  of  inward  and  outward  setting,  from  which  we 
separate  the  wolf  and  the  tree.  If  the  real  as  it  appears  is 
yi  =  a  b  c  d  efg  h,  then  our  judgment  is  nothing  but  X  =  a,  or 
X  =  a-b.  But  a-b  by  itself  has  never  been  given,  and  is  not 
what  appears.  It  was  in  the  fact  and  we  have  taken  it  out. 
It  was  of  the  fact  and  we  have  given  it  independence.  We 
have  separated,  divided,  abridged,  dissected,  we  have  mutilated 
the  given.*  And  we  have  done  this  arbitrarily  :  we  have 
selected  what  we  chose.  But,  if  this  is  so,  and  if  every 
analytic  judgment  must  inevitably  so  alter  the  fact,  how  can 
it  any  longer  lay  claim  to  truth } 

§  63.  No  doubt  we  shall  be  told,  "  This  is  idle  subtlety.    The 

judgment  does  not  copy  the  whole  perception,  but  why  should 

it  do  so }     What  it  does  say,  and  does  reproduce,  at  all  events 

is  there.     Fact  is  fact,  and  given  is  given.     They  do  not  cease 

*  Cf.  here  Lotze's  admirable  chapter,  Logik,  II.  VIII. 


Chap.  II.]  FORMS   OF  JUDGMENT.  95 

to  be  such  because  something  beside  themselves  exists.  To 
maintain  that '  There  is  a  wolf '  is  false,  because  an  abstract  wolf 
is. not  given  entirely  by  itself,  is  preposterous  and  ridiculous." 
And  I  am  afraid  that  with  some  readers  this  will  end  the 
discussion.  But  to  those  who  are  willing  to  venture  further, 
I  would  suggest  as  encouragement  that  a  thing  may  seem 
ludicrous,  not  because  it  is  at  all  absurd  in  itself,  but  because 
it  conflicts  with  hardened  prejudice.  And  it  is  a  prejudice  of 
this  kind  that  we  have  now  encountered. 

§  64.\  It  is  a  very  common  and  most  ruinous  superstition 

to  suppose  that  analysis  is  no  alteration,  and  that,  whenever 

we  distinguish,  we  have  at  once  to  do  with  divisible  existence. 

It  is  an  immense  assumption  to  conclude,  when  a  fact  comes 

to  us  as  a  whole,  that  some  parts  of  it  may  exist  without  any 

sort   of  regard    for   the   rest.     Such  naive  assurance  of  the 

outward   reality   of    all    mental    distinctions,    such   touching 

confidence  in  the  crudest  identity  of  thought  and  existence, 

is  worthy  of  the  school  which  so  loudly  appeals  to  the  name 

of   Experience.     Boldly  stated  by  Hume  (cf.  Book    II.    II. 

Chap.  I.    §  5),  this  cardinal  principle  of  error  and  delusion 

has  passed  into  the  traditional  practice  of  the  school,  and  is 

believed  too  deeply  to  be  discussed  or  now  recognized.     The 

protestations  of  fidelity  to  fact  have  been  somewhat  obtrusive, 

but  self-righteous  innocence  and  blatant  virtue  have  served 

once  more  here  to  cover  the  commission  of  the  decried  offence 

in  its  deadliest  form.     If  it  is  true  in  any  sense  (and  I  will  not 

deny  it),  that  thought  in  the  end  is  the  measure  of  things, 

yet  at  least  this  is  false,  that  the  divisions  we  make  within 

a  whole   all  answer  to   elements   whose    existence   does   not 

depend  on  the  rest.     It  is  wholly  unjustifiable  to  take  up  a 

complex,  to  do  any  work  we  please  upon  it  by  analysis,  and 

then   simply  predicate   as   an    adjective   of  the   given   these 

results  of  our  abstraction.     These  products  were  never  there 

as  such,  and  in  saying,  as  we  do,  that  as  such  they  are  there, 

we  falsify  the   fact.     You   can  not   always  apply   in   actual 

experience  that  coarse  notion  of  the  whole  as  the  sum  of  its 

parts  into  which  the  school  of  "  experience  "  so  delights  to 

torture  phenomena.     If  it  is  wrong  in  physiology  to  predicate 

the  results,  that  are  reached  by  dissection,  simply  and  as  such 


96  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

of  the  living  body,  it  is  here  infinitely  more  wrong.  The 
whole  that  is  given  us  is  a  continuous  mass  of  perception  and 
feeling  ;  and  to  say  of  this  whole,  that  any  one  element  would 
be  what  it  is  there,  when  apart  from  the  rest,  is  a  very  grave 
assertion.  We  might  have  supposed  it  not  quite  self-evident, 
and  that  it  was  possible  to  deny  it  without  open  absurdity.* 

§  65.  I  should  like  to  digress  so  far  as  to  adduce  two 
examples  of  error,  which  follow  from  the  mistake  we  are 
now  considering.  When  we  ask  "  What  is  the  composition  of 
Mind,"  we  break  up  that  state,  which  comes  to  us  as  a  whole, 
into  units  of  feeling.  But  since  it  is  clear  that  these  units  by 
themselves  are  not  all  the  "  composition,"  we  are  forced  to 
recognize  the  existence  of  relations.  But  this  does  not 
stagger  us.  We  push  on  with  the  conceptions  we  have 
brought  to  the  work,  and  which  of  course  can  not  be  false, 
and  we  say,  Oh  yes,  we  have  here  some  more  units,  naturally 
not  quite  the  same  as  the  others,  and — voila  tout.  But  when 
a  sceptical  reader,  whose  mind  has  been  warped  by  a  different 
education,  attempts  to  form  an  idea  of  what  is  meant,  he  is 
somewhat  at  a  loss.  If  units  have  to  exist  together,  they 
must  stand  in  relation  to  one  another ;  and,  if  these  relations 
are  also  units,  it  would  seem  that  the  second  class  must  also 
stand  in  relation  to  the  first.  If  A  and  B  are  feelings,  and  if 
C  their  relation  is  another  feeling,  you  must  either  suppose 
that  component  parts  can  exist  without  standing  in  relation 
with  one  another,  or  else  that  there  is  2.  fresh  relation  between 
C  and  AB.  Let  this  be  D,  and  once  more  we  are  launched 
on  the  infinite  process  of  finding  a  relation  between  D  and 
C-AB ;  and  so  on  for  ever.  If  relations  are  facts  that  exist 
between  facts,  then  what  comes  between  the  relations  and  the 
other  facts }  The  real  truth  is  that  the  units  on  one  side, 
and  on  the  other  side  the  relation  existing  between  them,  are 
nothing  actual.  They  are  fictions  of  the  mind,  mere  dis- 
tinctions within  a  single  reality,  which  a  common  delusion 
erroneously  takes  for  independent  facts.  If  we  believe  the 
assurance  of  a  distinguished  Professor,t  this  burning  faith  in 
the  absurd  and  the  impossible,  which  was  once  the  privilege 

*  For  the  general  validity  of  Analysis  and  Abstraction  see  Book  III. 
t  Vid.  Huxley,  Hume^  pp.  52,  69. 


Chap.  II.]  FORMS   OF   JUDGMENT.  9/ 

and  the  boast  of  theology,  can  now  not  be  acquired  anywhere 
outside  the  sacred  precincts  of  the  laboratory.  I  am  afraid  it 
is  difficult  to  adopt  such  an  optimistic  conclusion. 

§  66.  And  perhaps  I  may  be  pardoned  if,  by  another  illustra- 
tion, I  venture  to  show  how  entirely  the  mind  which  is  purified 
by  science  can  think  in  accordance  with  orthodox  Christianity. 
In  the  religious  consciousness  God  and  Man  are  elements  that 
are  given  to  us  in  connection.  But,  reflecting  on  experience, 
we  make  distinctions,  and  proceed  as  above  to  harden  these 
results  of  analysis  into  units.  We  thus  have  God  as  an  unit 
on  one  side,  and  Man  again  as  an  unit  on  the  other :  and  then 
we  are  puzzled  about  their  relation.  The  relation  of  course 
must  be  another  unit,  and  we  go  on  to  find  that  we  should 
like  something  else,  to  mediate  once  more,  and  go  between 
this  product  and  what  we  had  at  first.  We  fall  at  once  into 
the  infinite  process,  and,  having  taken  up  with  polytheism,  the 
length  we  go  is  not  a  matter  of  principle. 

§  6"].  To  return  to  the  analytic  judgment.  When  I  say 
"  There  is  a  wolf,"  the  real  fact  is  a  particular  wolf,  not  like 
any  other,  in  relation  to  this  particular  environment  and  to 
my  internal  self,  which  is  present  in  a  particular  condition  of 
feeling  emotion  and  thought.  Again,  when  I  say  "  I  have  a 
toothache,"  the  fact  once  more  is  a  particular  ache  in  a  certain 
tooth,  together  with  all  my  perceptions  and  feelings  at  that 
given  moment.  The  question  is,  when  I  take  in  my  judg- 
ment one  fragment  of  the  whole,  have  I  got  the  right  to 
predicate  this  of  the  real,  and  to  assert  "  It,  as  it  is,  is  a  fact  of 
sense  "  ?  Now  I  am  not  urging  that  the  analytic  judgment  is 
in  no  sense  true.  I  am  saying  that,  if  you  take  it  as  asserting 
the  existence  of  its  content  as  given  fact,  your  procedure  is 
unwarranted.  And  I  ask,  on  what  principle  do  you  claim  the 
right  of  selecting  what  you  please  from  the  presented  whole 
and  treating  that  fragment  as  an  actual  quality }  It  certainly 
does  not  exist  by  itself,  and  how  do  you  know  that,  when  put 
by  itself,  it  could  be  a  quality  of  this  reality  ?  The  sensible 
phenomenon  is  what  it  is,  and  is  all  that  it  is  ;  and  anything 
less  than  itself  must  surely  be  something  else.  A  fraction  of 
the  truth,  here  as  often  elsewhere,  becomes  entire  falsehood, 
because  it  is  used  to  qualify  the  whole. 

H 


98  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

§  68.  The  analytic  judgment  is  not  truQ  per  se.  It  can  not 
stand  by  itself.  Asserting,  as  it  does,  of  the  particular 
presentation,  it  must  always  suppose  a  further  content,  which 
falls  outside  that  fraction  it  affirms.  What  it  says  is  true,  if 
true  at  all,  because  of  something  else.  The  fact  it  states  is 
really  fact  only  in  relation  to  the  rest  of  the  context,  and  only 
because  of  the  rest  of  that  context.  It  is  not  true  except 
under  that  condition.  So  we  have  a  judgment  which  is  really 
conditioned,  and  which  is  false  if  you  take  it  as  categorical. 
To  make  it  both  categorical  and  true,  you  must  get  the 
condition  inside  the  judgment.  You  must  take  up  the  given 
as  it  rellly  appears,  without  omission,  unaltered,  and  un- 
mutilated.     And  this  is  impossible. 

§  69.  For  ideas  are  not  adequate  to  sensible  perception, 
and,  beyond  this  obstacle,  there  are  further  difficulties.  The 
real,  which  appears  within  the  given,  can  not  possibly  be 
confined  to  it.  Within  the  limit  of  its  outer  edges  its 
character  gives  rise  to  the  infinite  process  in  space  and  time. 
Seeking  there  for  the  simple,  at  the  end  of  our  search  we  still 
are  confronted  by  the  composite  and  relative.  And  the 
outer  edges  themselves  are  fluent.  They  pass  for  ever  in 
time  and  space  into  that  which  is  outside  them.  It  is  true 
that  the  actual  light  we  see  falls  only  upon  a  limited  area  ; 
but  the  continuity  of  the  element,  the  integrity  of  the  context, 
forbids  us  to  say  that  this  illuminated  section  by  itself  is  real. 
The  reference  of  the  content  to  something  other  than  itself 
lies  deep  within  its  internal  nature.  It  proclaims  itself  to  be 
adjectival,  to  be  relative  to  the  outside  ;  and  we  violate  its 
essence  if  we  try  to  assert  it  as  having  existence  entirely  in 
its  own  right,  f  Space  and  time  have  been  said  to  be  "  prin- 
ciples of  individuation."  It  would  be  truer  to  say  they  are 
principles  of  relativity.  They  extend  the  real  just  as  much 
as  they  confine  it.    ) 

I  do  not  mean  that  past  and  future  are  actually  given,  and 
that  they  come  within  the  circle  of  presentation.  I  mean 
that,  although  they  can  not  be  given,  the  given  would  be 
destroyed  by  their  absence.  If  real  with  them,  it  would  not 
be  given ;  and,  given  without  them,  it  is  for  ever  incomplete 
and  therefore  unreal.     The  presented  content  is,  in  short,  not 


Chap.  II.]  FORMS   OF  JUDGMENT.  99 

compatible  with  its  own  presentation.  It  involves  a  contra- 
diction, and  might  at  once  on  that  ground  be  declared  to  be 
unreal.  But  it  is  better  here  to  allow  it  free  course,  and  to 
suffer  it  to  develope  by  an  impossible  consequence  its  inherent 
unsoundness. 

I  §  70.  We  saw  that  you  can  not  ascribe  to  the  real  one  part 
of  what  is  given  in  present  perception.  And  now  we  must 
go  further.  Even  if  you  could  predicate  the  whole  present 
content,  yet  still  you  would  fail  unless  you  asserted  also  both 
the  past  and  the  future.  You  can  not  assume  (or  I,  at  least, 
do  not  know  your  right  to  assume)  that  the  present  exists 
independent  of  the  past,  and  that,  taking  up  one  fragment  of 
the  whole  extension,  you  may  treat  this  part  as  self-subsistent, 
as  something  that  owes  nothing  to  its  connection  with  the 
rest.  If  your  judgment  is  to  be  true  as  well  as  categorical, 
you  must  get  the  conditions  entirely  within  it.  And  here  the 
conditions  are  the  whole  extent  of  spaces  and  times  which 
are  required  to  make  the  given  complete.  The  difficulty  is 
insuperable.  It  is  not  merely  that  ideas  can  not  copy  facts  of 
sense.  It  is  not  merely  that  our  understandings  are  limited, 
that  we  do  not  know  the  whole  of  the  series,  and  that  our 
powers  are  inadequate  to  apprehend  so  large  an  object.  No 
possible  mind  could  represent  to  itself  the  completed  series  of 
space  and  time  ;  since,  for  that  to  happen,  the  infinite  process 
must  have  come  to  an  end,  and  be  realized  in  a  finite  result. 
And  this  cannot  be.  It  is  not  merely  inconceivable  psycho- 
logically ;  it  is  metaphysically  impossible. 

§  71.  Our  analytic  judgments  are  hence  all  either  false  or 
conditioned.  "  But  conditioned',^  I  may  be  told,  "  is  a  doubtful 
phrase.  After  all  it  is  not  the  same  as  hypothetical.  A 
thing  is  conditio?^^/  on  account  of  a  supposal,  but  on  the 
other  hand  it  is  conditio;^^*^?  by  a  fact.  We  have  here  the 
difference  between  'if  and  'because.'  When  a  statement  is 
true  in  consequence  of  the  truth  of  another  statement,  they 
both  are  categorical."  I  quite  admit  the  importance  of  the 
distinction,  and  must  recur  to  it  hereafter  (Chap.  VII.  §  10). 
But  I  deny  its  relevancy  for  our  present  purpose. 

The  objection  rests  on  the  following  contention.  "Ad- 
mitted that  in   the    series    of  phenomena   every  element   is 

H  2 


lOO  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

relative  to  the  rest  and  is  because  of  something  else,  yet  for 
all  that  the  judgment  may  be  categorical.  The  something 
else,  though  we  are  unable  to  bring  it  within  the  judgment, 
though  we  can  not  in  the  end  ever  know  it  at  all  and  realize  it 
in  thought,  is,  for  all  that,  fact.  And,  this  being  so,  the  state- 
ment is  true  ;  since  it  rests  in  the  end,  not  at  all  on  an  '  if '  but 
upon  a  '  because,'  which,  although  unknown,  is  none  the  less 
real.  Let  the  analytic  judgment  admit  its  relativity,  let  it 
own  its  adjectival  and  dependent  character,  and  it  surely 
saves  itself  and  remains  categorical." 

But  even  this  claim  it  is  impossible  to  admit.  I  will  not 
raise  a  difficulty  about  the  "  because  "  which  is  never  realized, 
and  the  fact  which  can  never  be  brought  before  the  mind. 
My  objection  is  more  fatal.  In  the  present  case  there  is  no 
because,  and  there  is  no  fact. 

We  are  fastened  to  a  chain,  and  we  wish  to  know  if  we 
are  really  secure.  What  ought  we  to  do  ?  Is  it  much  use  to 
say,  "  This  link  we  are  tied  to  is  certainly  solid,  and  it  is  fast 
to  the  next,  which  seems  very  strong  and  holds  firmly  to  the 
next :  beyond  this  we  can  not  see  more  than  a  certain 
moderate  distance,  but,  so  far  as  we  know,  it  all  holds  to- 
gether "  ?  The  practical  man  would  first  of  all  ask,  "  Where 
can  I  find  the  last  link  of  my  chain  ?  When  I  know  that  is 
fast,  and  not  hung  in  the  air,  it  is  time  enough  to  inspect  the 
connection."  But  the  chain  is  such  that  every  link  begets, 
so  soon  as  we  come  to  it,  a  new  one ;  and,  ascending  in  our 
search,  at  each  remove  we  are  still  no  nearer  the  last  link  of 
all,  on  which  everything  depends.  The  series  of  phenomena 
is  so  infected  with  relativity,  that,  while  it  is  itself,  it  can  never 
be  made  absolute.  Its  existence  refers  itself  to  what  is 
beyond,  and,  did  it  not  do  so,  it  would  cease  to  exist.  A  last 
fact,  a  final  link,  is  not  merely  a  thing  which  we  can  not  know, 
but  a  thing  which  could  not  possibly  be  real.  Our  chain  by 
its  nature  can  not  have  a  support.  Its  essence  excludes  a 
fastening  at  the  end.  We  do  not  merely  fear  that  it  hangs 
in  the  air,  but  we  know  it  must  do  so.  And  when  the  end  is 
^Unsupported,  all  the  rest  is  unsupported.  Hence  our  con- 
diiioned  truth  is  only  conditioiiaL  It  avowedly  depends  on 
what  is  not  fact,  and  it  is  not  categorically  true.     Not  standing 


Chap.  1L]  FORMS  OF  JUDGMEN'T.  lOl" 

by  itself,  it  hangs  from  a  supposition  ;  or  perhaps  a  still 
.  worse  destiny  awaits  it,  it  hangs  from  nothing  and  falls 
j  altogether. 

§  72.  It  will  be  said,  of  course,  that  this  is  mere  meta- 
physics. Given  is  given,  and  fact  is  fact.  Nay  we  ourselves 
distinguished  above  the  individual  from  the  hypothetic  judg- 
ment, on  the  ground  that  the  former  went  to  perception,  and 
that  we  found  there  existing  the  elements  it  asserted.  Such  a 
plain  distinction  should  not  be  ignored,  because  it  disappears 
in  an  over-subtle  atmosphere.  But  I  do  not  wish  to  take 
back  this  distinction.  It  is  valid  at  a  certain  level  of  thought ; 
and,  for  the  ordinary  purposes  of  logical  enquiry,  individual 
judgments,  both  synthetic  and  analytic,  may  conveniently  be 
taken  as  categorical,  and  in  this  sense  opposed  to  universal 
judgments. 

But,  when  we  go  further  into  the  principles  of  logic,  and 
are  forced  to  consider  how  these  classes  of  judgment  stand  to 
one  another,  we  are  certain  to  go  wrong,  if  we  have  not  raised 
such  questions  as  the  above.  It  is  not  enough  to  know  that 
we  have  a  ground  of  distinction.  We  must  ask  if  it  is  a  true 
ground.  Is  it  anything  more  than  a  point  to  reckon  from  } 
Is  it  also  fact }  Does  the  light  of  presence,  which  falls  on  a 
content,  guarantee  its  truthfulness  even  if  we  copy?  Are 
the  presented  phenomenon,  and  series  of  phenomena,  actual 
realities  .'*  And,  we  have  seen,  they  are  not  so.  The  given  in 
sense,  if  we  could  seize  it  in  judgment,  would  still  disappoint 
us.  It  is  not  self-existent  and  is  therefore  unreal,  and  the 
reality  transcends  it,  first  in  the  infinite  process  of  phenomena, 
and  then  altogether.  The  real,  which  (as  we  say)  appears 
in  perception,  is  neither  a  phenomenon  nor  a  series  of 
phenomena. 

§  73.'Tt'may  be  said  "This  is  only  the  product  of  reflec- 
tion. If  we  are  content  to  take  the  facts  as  they  come  to  us, 
if  we  will  only  leave  them  just  as  we  feel  them,  they  never 
disappoint  us.  They  neither  hang  by  these  airy  threads 
from  the  past,  nor  perish  internally  in  a  vanishing  network 
of  never-ending  relations  between  illusory  units.  The  real, 
as  it  simply  comes  to  us  in  sense,  has  nothing  of  all  this.  It 
is   one   with   itself,    individual,    and    complete,  absolute    and 


102  ■  ■  •    'THfe  PRINCIPLES   OF   LOGIC.  [Book  I. 

categorical."  We  are  not  here  concerned  to  controvert  this 
statement.  We  are  not  called  on  to  ask  if  anything  that  is  given 
is  given  apart  from  intellectual  modification,  if  there  is  any  pro- 
duct we  can  observe  and  watch,  with  which  we  have  not  already 
interfered.  We  have  no  motive  here  to  raise  such  an  issue  ; 
nor  again  do  we  rejoice  in  that  infatuation  for  intellect,  and 
contempt  for  feeling,  which  is  supposed  to  qualify  the  com- 
petent metaphysician.  Nor  will  we  pause  to  argue  that 
frustrated  Reeling  itself  heads  the  revolt  against  the  truth  of 
sense.  It  was  a  baffled  heart  that  first  raised  the  suspicion  of 
a  cheated  head,    j 

You  may  say,  if  you  like,  that  the  real  just  as  we  feel  it  is 
true.  But,  if  so,  then  <3:// judgments  are  surely  false,  and  your 
singular  judgment  goes  with  the  rest.  For  our  present  pur- 
pose we  may  admit  your  assertion,  but,  if  it  is  meant  as  an 
objection,  we  answer  it  by  asking  the  question.  What  then  ? 
Who  is  it  who  says  this  ?  Who  counts  himself  so  free  from 
the  sin  of  reflection  as  to  throw  this  stone  ?  Some  man  no 
doubt  who  has  not  an  idea  of  the  consequences  of  his  saying  ; 
some  writer  whose  pages  are  filled  with  bad  analysis  and 
dogmatic  metaphysics ;  some  thinker  whose  passion  for 
"experience"  is  mere  prejudice  in  favour  of  his  own  one-sided 
theory,  and  whose  loyal  regard  for  the  sensible  fact  means 
inability  to  distinguish  it  from  that  first  result  of  a  crude 
reflection  in  which  he  sticks. 

For  the  present  we  may  assume,  what  metaphysics  would 
discuss,  that  phenomena  are  what  we  can  not  help  thinking 
them  in  the  end,  and  that  the  last  result  of  our  thought  is  true, 
or  all  the  truth  we  have.  It  is  not  the  beginning  but  the  end 
of  reflection  which  is  valid  of  the  real ;  or  we  are  such  at  least 
that  our  minds  are  unable  to  decide  for  aught  else.  And  we 
have  seen  that  our  thinking  about  the  real,  if  we  remain  at 
the  level  of  the  analytic  judgment,  will  not  stand  criticism. 
The  result  of  our  later  and,  we  are  forced  to  believe,  our 
better  reflection  is  conviction  that  at  least  this  judgment 
is  not  true.  To  assert  as  a  quality  of  the  real  either  the 
whole  or  part  of  the  series  of  phenomena,  is  to  make  a  false 
assertion. 

§  74.  The  reality  is  given  and  is  present  to  sense  ;  but  you 


Chap.  II.]  FORMS   OF  JUDGMENT.  IO3 

cannot,  as  we  saw  (§  11),  convert  this  proposition,  and  say 
Whatever  is  present  and  given  is,  as  such,  real.  The  present 
is  not  merely  that  section  of  the  phenomena  in  space  and  time 
which  it  manifests  to  us.  It  is  not  simply  the  same  as  its 
appearance..  Presence  is  our  contact  with  actual  reality  ;  and 
the  reception  of  the  elements  of  sensuous  perception  as 
existing  facts  is  one  kind  of  contact,  but  it  is  not  the  only 
kind. 

In  hypothetical  judgments  there  is  a  sense  in  which  the 
real  is  given  ;  for  we  feel  its  presence  in  the  connection  of  the 
elements,  and  we  ascribe  the  ground  to  the  real  as  its  quality. 
Hypothetical  judgments  in  the  end  must  rest  on  direct 
presentation,  though  from  that  presentation  we  do  not  take 
the  elements  and  receive  them  as  fact.  It  is  merely  their 
synthesis  which  holds  good  of  the  real  (§  50),  and  it  is  in  our 
perception  of  the  ground  of  that  synthesis  that  we  come  into 
present  contact  with  reality.  I  will  not  ask  if  this  contact  is 
more  direct  than  that  which  supports  the  analytical  judgment. 
But  at  all  events  we  may  say  it  is  truer  ;  since  truth  is  what 
is  true  of  the  ultimate  real.  A  supersensible  ultimate  quality 
is  not  much  to  assert,  but  at  all  events  the  assertion  seems 
not  false.  On  the  other  hand  the  categoric  affirmation  of  the 
analytic  judgment  of  sense  we  know  is  not  true.  The 
content  it  asserts  we  know  is  not  real.  And,  taken  in  this 
sense,  there  remains  no  hope  for  the  individual  judgment. 

§  75.  There  is  no  hope  for  it  at  all,  till  it  abates  its  pre- 
tensions, till  it  gives  up  its  claims  to  superiority  over  the 
hypothetic  judgment,  and  is  willing  to  allow  that  it  itself  is 
no  more  than  conditional.  But  it  does  not  yet  know  the 
degradation  that  awaits  it.  It  may.  say,  "  It  is  true  that  I 
am  not  categorical.  My  content  is  conditioned,  and  the 
*  because '  has  turned  round  in  my  hands  into  '  if.'  But  at 
least  I  am  superior  to  the  abstract  hypothetical.  For  in  that 
the  elements  are  not  even  asserted  to  have  reality,  whereas, 
subject  to  the  condition  of  the  rest  of  the  series,  I  at  least 
assert  my  content  to  be  fact.  So  far  at  least  I  affirm 
existence  and  maintain  my  position." 

But  this  claim  is  illusory,  for  if  the  individual  judgment 
becomes  in  this  way  hypothetical,  it  does  not  assert  that  its 


104  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

content  has  any  existence.  If  it  did  it  would  contradict  itself, 
and  I  will  endeavour  to  explain  this. 

The  content  a-b  in  the  categoric  judgment  was  directly 
ascribed  to  real  existence.  The  abstract  universal  judgment 
a-b  does  not  ascribe  either  a  or  b  ox  their  connection  to  the 
real  ;  it  merely  ascribes  a  quality  x.  The  question  now  is 
Can  you  save  the  categoric  a-b  by  turning  it  into  a  hypo- 
thetical in  which  a-b  is  still  asserted  of  existence,  though 
under  a  condition, — or  must  it  become  the  universal  a-b 
which  ignores  existence  ?  In  the  latter  case  it  would  simply 
mean,  "Given  a^  then  b^  But  in  the  former  it  would  run, 
"  Given  something  else,  then  a-b  exists."  This  illusory  claim 
is  not  very  pretentious,  but  I  wish  to  show  that  it  is  suicidal. 

Drobisch  {Logik,  §  56),  following  Herbart  (I.  106),  trans- 
lates the  judgment  "  P  exists,"  into  "  If  anything  exists  any- 
where, then  P  exists."  I  consider  this  translation  to  be 
incorrect ;  for  it  covertly  assumes  that  something  does  exist, 
and  hence  is  in  substance  still  categorical.  And  if  we  apply 
this  translation  to  the  facts  of  sense,  then  what  is  really 
supposed  is  the  completed  series  of  other  phenomena,  and 
the  translation  must  run  thus,  "  If  everything  else  exists,  then 
P  exists."  But  the  assertion  is  now  suicidal,  for  "  everything 
else,"  we  have  seen  above  (§  70),  can  never  be  a  real  fact. 
The  hypothetical  assertion  of  existence  is  therefore  made 
dependent  on  a  condition  which  can  not  exist.  Now  it  is 
not  true  that  the  consequence  of  a  false  hypothesis  must 
be^  false  ;  but  it  certainly  is  true,  when  an  impossible  ground 
is  laid  down  as  the  sole  condition  of  existence,  that  in 
a  roundabout  way  existence  is  denied.  The  individual 
judgment,  we  saw,  was  false  when  taken  categorically.  And 
now,  we  see,  when  taken  hypothetically,  instead  of  assert- 
ing it  rather  denies,  or  at  least  suggests  that  denial  may 
be  true. 

§  76.  The  only  hope  for  the  singular  judgment  lies  in 
complete  renunciation.  It  must  admit  that  the  abstract, 
although  hypothetical,  is  more  true  than  itself  is.  It  must 
ask  for  a  place  in  the  same  class  of  judgment  and  be  content 
to  take  the  lowest  room  there.  It  must  cease  to  predicate 
its  elements  of  the  real,  and   must  confine  itself  to  asserting 


Chap.  II.]  FORMS   OF  JUDGMENT.  IO5 

their  connection  as  adjectives  generally,  and  apart  from 
particular  existence.  Instead  of  meaning  by  "  Here  is  a  wolf," 
or  "  This  tree  is  green,"  that  "  wolf "  and  "  green  tree  "  are  real 
facts,  it  must  affirm  the  general  connection  of  wolf  with 
elements  of  the  environment,  and  of  "  green  "  with  "  tree."  And 
it  must  do  this  in  an  abstract  sense,  without  any  reference 
to  the  particular  fact.  In  a  low  and  rudimentary  form 
it  thus  tends  to  become  a  scientific  law,  and,  entirely  giving 
up  its  original  claims,  it  now  sets  its  foot  on  the  ladder  of 
truth. 

§  TJ.  But  it  remains  upon  the  very  lowest  round.  Every 
judgment  of  perception  is  in  a  sense  universal,  and,  if  it  were 
not  so,  it  could  never  be  used  as  the  basis  of  inference.  The 
statement  goes  beyond  the  particular  case,  and  involves  a 
connection  of  adjectives  which  is  true  without  respect  to 
"  this  "  "  here  "  and  "  now."  If  you  take  it  as  ascribing  its  ideal 
content  to  this  reality,  it  no  doubt  is  singular,  but,  if  you 
take  it  as  asserting  a  synthesis  inside  that  ideal  content,  it 
transcends  perceptions  ;  for  anywhere  else  with  the  same 
conditions  the  same  result  would  hold.  The  synthesis  is 
true,  not  here  and  now,  but  universally. 

And  yet  its  truth  remains  most  rudimentary,  for  the  con- 
nection of  adjectives  is  immersed  in  matter.  The  content  is 
full  of  indefinite  relations,  and,  in  the  first  vague  form  which 
our  statements  assume,  we  are  sure  on  the  one  hand  to  take 
into  the  assertion  elements  which  have  nothing  to  do  with 
the  synthesis,  and,  on  the  other  hand,  to  leave  out  something 
which  really  helps  to  constitute  its  necessity.  We  say  for 
example,  "  This  body  putrefies  ; "  but  it  does  not  putrefy 
because  it  is  this  body.  The  real  connection  is  far  more 
abstract.  And  again  on  the  other  hand  it  would  not  putrefy 
simply  because  of  anything  that  it  is,  and  without  foreign 
influence.  In  the  one  case  we  add  irrelevant  details,  and  in 
the  other  we  leave  out  an  essential  factor.  In  the  one  case 
we  say,  "  The  real  is  such  that,  given  abc,  then  d  will  follow," 
when  the  connection  is  really  nothing  but  a-d.  In  the  other 
case  we  say,  "  The  connection  is  a-b^'  when  a  is  not  enough  to 
necessitate  b,  and  the  true  form  of  synthesis  is  a  (c)-b. 
Measured  by  a  standard  of  scientific  accuracy,  the  first  forms 


I06        -  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

of  our  truths  must  always  be  false.  They  say  too  little,  or 
too  much,  or  both  ;  and  our  upward  progress  must  consist  in 
correcting  them  by  removing  irrelevancies  and  filling  up  the 
essential.* 

§  y8.  The  practice  of  science  confirms  the  result  to 
which  our  long  analysis  has  brought  us  ;  for  what  is  once 
true  for  science  is  true  for  ever.  Its  object  is  not  to 
record  that  complex  of  sensible  phenomena,  which  from 
moment  to  moment  perception  presents  to  us.  It  desires  to 
get  a  connection  of  content,  to  be  able  to  say.  Given  this  or 
that  element,  and  something  else  universally  holds  good. 
It  endeavours  to  discover  those  abstract  elements  in  their 
full  completeness,  and  to  arrange  the  lower  under  the  higher. 
Recurring  to  a  term  we  used  before,  we  may  say  its  aim 
is  to  purge  out  "thisness,"  to  reconstruct  the  given  as  ideal 
syntheses  of  abstract  adjectives.  Science  from  the  first  is  a 
process  of  idealization  ;  and  experiment,  Hegel  has  long  ago 
told  us,  is  an  idealizing  instrument, -for  it  sublimates  fact  into 
general  truths. 

Both  in  common  life  and  in  science  alike,  a  judgment  is  at 
once  applied  to  fresh  cases.  It  is  from  the  first  an  universal 
truth.  If  it  really  were  particular  and  wholly  confined  to  the 
case  it  appears  in,  it  might  just  as  well  have  never  existed, 
for  it  could  not  be  used.  A  mere  particular  judgment  does 
not  really  exist,  and,  if  it  did  exist,  would  be  utterly  worth- 
less (cf.  Chap.  VI.  and  Book  II.). 

§  79.  It  is  time  that  we  collected  what  result  has  come 
from  these  painful  enquiries.  If  we  consider  the  ultimate 
truth  of  assertions,  then,  so  far  as  we  have  gone,  the  cate- 
gorical judgment  in  its  first  crude  form  has  entirely  dis- 
appeared.    The  distinction  between  individual  and  universal, 

;  categorical  and  hypothetical,  has  been  quite  broken  through. 

f-AU  judgments  are  categorical,  for  they  all  do  affirm  about 
the  reality,  and  assert  the  existence  of  a  quality  in  that. 
Again,  all  are  hypothetical,  for  not  one  of  them  can  ascribe  to 

{  real  existence  its  elements  as  such.     All  are  individual,  since 

'  the  real  which  supports  that  quality  which  forms  the  ground 

*  For  explanation  and  illustration  I  must  refer  to  Lotze's  admirable 
chapter  cited  above. 


Chap.  II.]  FORMS   OF  JUDGMENT.  10/ 

of  synthesis,  is  itself  substantial.  Again  all  are  universal, 
since  the  synthesis  they  affirm  holds  out  of  and  beyond  the 
particular  appearance.  They  are  every  one  abstract,  for  they 
disregard  context,  they  leave  out  the  environment  of  the 
sensible  complex,  and  they  substantiate  adjectives.  And 
yet  all  are  concrete,  for  they  none  of  them  are  true  of  any- 
thing else  than  that  individual  reality  which  appears  in  the 
sensuous  wealth  of  presentation. 

§  80.  But,  if  we  remain  at  a  lower  point  of  view,  if  we 
agree  not  to  scrutinize  the  truth  of  judgments,  and  if  we  allow 
assertions  as  to  particular  fact  to  remain  in  the  character 
which  they  claim  for  themselves,  in  that  case  our  result  will 
be  somewhat  different.  Abstract  judgments  will  all  be 
hypothetical,  but  the  judgments  that  analyze  what  is  given  in 
perception  will  all  be  categorical.  Synthetic  judgments 
about  times  or  spaces  beyond  perception  will  come  in  the 
middle.  They  involve  an  inference  on  the  strength  of  an 
universal,  and  so  far  they  must  have  a  hypothetical  character. 
They  again  involve  an  awkward  assumption,  for  you  can  go  to 
them  only  through  the  identity  of  an  element  in  the  several 
contents  of  a  perception  and  an  idea.  As  however,  on  the 
strength  of  this  assumption,  the  universal  is  brought  into 
connection  with  the  given,  the  "if"  is  so  turned  into  a 
"  because,"  and  the  synthetic  judgment  may  be  called  cate- 
gorical. The  two  classes,  so  far,  will  on  one  side  be  assertions 
about  particular  fact  and  on  the  other  side  abstract  or  adjectival 
assertions.  The  latter  are  hypothetical,  and  the  first  cate- 
gorical. 

§  81.  We  have  all  this  time  omitted  to  consider  that  class 
of  judgment  which  makes  an  assertion  about  an  individual 
(which  is  not  a  phenomenon  in  space  or  time  (§  41).  Is  it 
possible  that  here  we  have  at  last  a  judgment  which  is  not  in 
any  sense  hypothetical .?  Can  one  of  these  directly  predicate 
of  the  individual  real  an  attribute  which  really  and  truly 
belongs  to  it }  May  we  find  here  a  statement  which  asserts 
the  actual  existence  of  its  elements,  and  which  is  not  false  ? 
Can  truth  categorical  be  finally  discovered  in  some  such 
judgment  as  "The  self  is  real,"  or  "Phenomena  are  nothing 
beyond  the  appearance  of  soul  to  soul  "  .?     It  would  seem  to 


I08  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

US  strange  indeed  if  this  were  so,  and  yet  after  all  perhaps  it 
is  our  minds  that  are  really  estranged. 

But  we  can  not  here  attempt  to  answer  these  questions. 
We  can  only  reply  when  asked  where  truth  categorical 
dwells,  Either  here  or  nowhere. 


(     I09    ) 

>^  OP  THE 

^univb^sity' 

CHAPTER  III. 

THE  NEGATIVE  JUDGMENT. 

§  I.  After  the  long  discussion  of  the  preceding  chapter, 
we  are  so  familiar  with  .the  general  character  of  judgment  that 
we  can  afford  to  deal  rapidly  with  particular  applications. 
Like  every  other  vairiety,  the  negative  judgment  depends  on 
the  real  which  appears  in  perception.  In  the  end  it  consists 
in  the  declared  refusal  of  that  subject  to  accept  an  ideal 
n:ontent.  The  suggestion  of  the  real  as  qualified  and  deter-" 
mined  in  a  certain  way,  -and  the  exclusion  of  that  suggestion 
by  its  application  to  actual  reality,  is  the  proper  essence  of 
^the  negative  judgment. 

§  2.  Though  denial,  as  we  shall  see,  can  not  be  reduced  to 
or  derived  from  affirmation,  yet  it  would  probably  be  wrong 
to  consider  the  two  as  co-ordinate  species.  It  is  not  merely  as 
we  shall  see  lower  down  (§  7),  that  negation  presupposes 
a  positive  ground.  It  stands  at  a  different  level  of  reflection. 
For  in  affirmative  judgment  we  are  able  to  attribute  the 
content  directly  to  the  real  itself  To  have  an  idea,  or  a 
synthesis  of  ideas,  and  to  refer  this  as  a  quality  to  the  fact 
that  appears  in  presentation,  was  all  that  we  wanted.  But, 
in  negative  judgment,  this  very  reference  of  content  to  reality 
must  itself  be  an  idea.  Given  X  the  fact,  and  an  idea  a  —  b, 
you  may  at  once  attribute  ^  —  ^  to  X ;  but  you  can  not  deny 
a  —  boi  X,  so  long  as  you  have  merely  X  and  a  —  b.  For,  in 
order  to  deny,  you  must  have  the  suggestion  of  an  affirmative 
relation.  The  idea  of  X,  as  qualified  hy  a  —  b,  which  we  may 
write  X  {a  —  b),  is  the  ideal  content  which  X  repels,  and  is  what 
we  deny  in  our  negative  judgment. 

It  may  be  said  no  doubt  that  in  affirmative  judgment  the 
real  subject  is  always  idealized.  We  select  from  the  whole  that 
appears  in  presentation,  and  mean  an  element  that  we  do  not 


no  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

mention  (Book  III.  I.  Chap.  VI.  §  1 2).  When  we  point  to  a  tree 
and  apply  the  word  "  green,"  it  may  be  urged  that  the  subject 
is  just,  as  ideal  as  when  the  same  object  rejects  the  offered 
suggestion  "yellow."  But  this  would  ignore  an  important 
difference.  The  tree,  in  its  presented  unity  with  reality,  can 
accept  at  once  the  suggested  quality.  I  am  not  always  forced 
to  suspend  my  decision,  to  wait  and  consider  the  whole  as 
ideal,  to  ask  in  the  first  place,  Is  the  tree  green  ?  and  then 
decide  that  the  tree  is  a  green  tree.  But  in  the  negative 
judgment  where  "yellow"  is  denied,  the  positive  relation  of 
"yellow"  to  the  tree  must  precede  the  exclusion  of  that 
relation.  The  judgment  can  never  anticipate  the  question. 
I  must  always  be  placed  at  that  stage  of  reflection  which 
sometimes  I  avoid  in  affirmative  judgment. 

§  3.  And  this  distinction  becomes  obvious,  if  we  go  back 
to  origins  and  consider  the  early  developement  of  each  kind. 
The  primitive  basis  of  affirmation  is  the  coalescence  of  idea 
with  perception.  But  mere  non-coalescence  of  an  idea  with 
perception  is  a  good  deal  further  removed  from  negation. 
It  is  not  the  mere  presence  of  an  unreferred  idea,  nor  its 
unobserved  difference,  but  it  is  the  failure  to  refer  it,  or 
identify  it,  which  is  the  foundation  of  our  first  denial.  The 
exclusion  by  presented  fact  of  an  idea,  which  attempted  to 
qualify  it,  is  what  denial  starts  from.  What  negation  must 
begin  with  is  the  attempt  on  reality,  the  baffled  approach  of  a 
qualification.  And  in  the  consciousness  of  this  attempt  is 
implied  not  only  the  suggestion  that  is  made,  but  the  subject  to 
which  that  suggestion  is  offered.  Thus  in  the  scale  of  reflection 
negation  stands  higher  than  mere  affirmation.  It  is  in  one 
sense  more  ideal,  and  it  comes  into  existence  at  a  later  stage 
of  the  developement  of  the  soul.* 

§  4.  But  the  perception  of  this  truth  must  not  lead  us  into 
error. /(^  We  must  never  say  that  negation  is  the  denial  of  an 
existing  judgment.  For  judgment,  as  we  know,  implies  belief; 
and  it  is  not  the  case  that  what  we  deny  we  must  once  have 
believed.  And  again,  since  belief  and  disbelief  are  incompatible, 
the  negative  judgment  would  in  this  way  be  made  to  depend 

♦  Compare  on  this  whole  subject  Sigwart,  Z^^//^,  I.  119  and  foil.     I 
do  not,  however,  wholly  accept  his  views. 


Chai'.  III.]  THE    NEGATIVE   JUDGMENT.  1 1 1 

on  an  element  which,  alike  by  its  existence  or  its  disappear- 
ance, would  remove  the  negation  itself.     What  we  deny  is  not 
the  reference  of  the  idea  to  actual  fact.     It  is  the  mere  idea  of  7 
the  fact,  as  so  qualified,  which  negation  excludes  ;  it  repels  the 
suggested  synthesis,  not  the  real  judgment. 

§  5.  .From  this  we  may  pass  to  a  counterpart  error.  If  it 
is  a  mistake  to  say  that  an  affirmative  judgment  is  presupposed 
in  denial,  it  is  no  less  a  mistake  to  hold  that  the  predicate 
alone  is  affected,  and  that  negation  itself  is  a  kind  of 
affirmation.  We  shall  hereafter  recognize  the  truth  which 
this  doctrine  embodies,  but,  in  the  form  it  here  assumes,  we 
can  not  accept  it.  The  exclusion  by  fact  of  an  approaching 
quality  is  a  process  which  calls  for  its  own  special  expression. 
And  when  we  are  asked  to  simplify  matters  by  substituting 
"  A  is  Not-B  "  for  "  A  is  not  B,"  we  find  an  obvious  difficulty. 
In  order  to  know  that  A  accepts  Not-B,  must  we  not 
already  have  somehow  learnt  that  A  excludes  B  }  And,  if  so, 
we  reduce  negation  to  affirmation  by  first  of  all  denying,  and 
then  asserting  that  we  have  denied, — a  process  which  no  doubt 
is  quite  legitimate,  but  is  scarcely  reduction  or  simplifica- 
tion. 

§  6.  There  is  a  further  objection  we  shall  state  hereafter  ^ 
(§  16)  to  the  use  of  Not-B  as  an  independent  predicate. 
But  at  present  we  must  turn  to  clear  the  ground  of  another 
error.  We  may  be  told  that  negation  "affects  only  the  j^ 
copula  ; "  and  it  is  necessary  first  to  ask  what  this  means.  If 
it  means  what  it  says,  we  may  dismiss  it  at  once,  since 
the  copula  may  be  wanting.  If  the  copula  is  not  there 
when  I  positively  say  "Wolf,"  so  also  it  is  absent  when  I 
negatively  say  "  No  wolf."  But,  if  what  is  meant  is  that  denial 
and  assertion  are  two  sorts  of  judgment,  which  stand  on  a 
level,  then  the  statement  once  again  needs  correction.  It  is 
perfectly  true  that  these  two  different  sorts  of  judgment 
exist.  The  affirmative  judgment  qualifies  a  subject  by  the 
attribution  of  a  quality,  and  the  negative  judgment  qualifies  a 
subject  by  the  explicit  rejection  of  that  same  quality.  We 
have  thus  two  kinds  of  asserted  relation.  But  the  mistake 
arises  when  we  place  them  on  a  level.  It  is  not  only 
true  that,  as  a  condition  of  denial,  we  must  have  already  a 


112  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

suggested   synthesis,   but   there   is  in    addition    another   ob- 
jection.    The  truth  of  the  negative  may  be  seen  in  the  end 
to   lie  in  the   affirmation  of  a  positive  quality ;    and   hence 
assertion  and  denial   cannot  stand  on  one   level.     In  "  A  is 
not    B "    the   real   fact   is   a   character  x  belonging    to    A, 
and  which  is  incompatible  with  B.     The  basis  of  negation 
is  really  the  assertion   of  a  quality  that  excludes  {x).     It  is 
not,  as  we  saw,  the  mere  assertion  of  the  quality  of  exclusion 
(Not-B). 
^      §  7.  Every  negation  must  have  a  ground,  and  this  ground 
^is   positive.     It   is   that   quality  x  in   the   subject   which  is 
incompatible  with  the  suggested  idea.     A  is  not  B  because  A 
is  such  that,  if  it  were  B,  it  would  cease  to  be  itself     Its 
quality  would  be  altered  if  it  accepted  B ;  and  it  is  by  virtue  of 
this  quality,  which  B  would  destroy,  that  A  maintains  itself 
and   rejects   the   suggestion.     In   other  words  its  quality  x 
^   and  B   are  disparate  or  discrepant.      And  we  cannot  deny 
'   B  without  affirming  in  A  the  pre-existence  of  this  disparate 
quality. 

But  in  negative  judgment  x  is  not  made  explicit.  We  do 
not  say  what  there  is  in  A  which  makes  B  incompatible.  We 
often,  if  asked,  should  be  unable  to  point  out  and  to  distinguish 
this  latent  hindrance :  and  in  certain  cases  no  effort  we  could 
make  would  enable  us  to  do  this.  If  B  is  accepted,  A  loses 
its  character  ;  and  in  these  cases  we  know  no  more.  The 
ground  is  not  merely  unstated  but  is  unknown. 

§  8.  The  distinctions  of  "  privation  "  and  "  opposition  "  (Sig- 
wart,  128  foil.)  do  not  alter  the  essence  of  what  we  have  laid 
down.  Z'  In  a  privative  judgment  the  predicate  "  red  "  would  be 
denied  of  the  subject  simply  on  the  ground  that  red  was 
not  there.  The  subject  might  be  wholly  colourless  and  dark. 
But  if  "red"  were  denied  on  the  ground  that  the  subject  was 
coloured  green,  it  would  be  the  presence  of  an  opposite  quality 
that  would  exclude,  and  the  judgment  would  then  be  based  on 
positive  opposition.  This  distinction  we  shall  find  in  another 
context  to  be  most  material  (cf  Chap.  VI.  and  Book  III.  11. 
Chap.  III.  §  20) ;  but,  for  our  present  purpose,  it  may  be  called 
irrelevant.  In  the  one  case  as  in  the  other,  the  subject  is 
taken  with  a  certain  character ;  and  by  addition  as  well  as  by 


Chap.  III.]  THE   NEGATIVE  JUDGMENT.  II 3 

diminution  that  individual  character  may  be  destroyed.  If 
a  body  is  not  red  because  it  is  uncoloured,  then  the  adding-on 
of  colour  would  destroy  that  body  as  at  present  we  regard  it. 
We  may  fairly  say  that,  if  the  predicate  were  accepted,  the 
subject  would  no  longer  be  the  subject  it  is.  And,  if  so,  in 
the  end  our  denial  in  both  cases  will  start  from  a  discrepant 
quality  and  character. 

§  9.  It  may  be  answered,  no  doubt,  that  the  subject,  as  it 
is  now  and  as  we  now  regard  it,  is  not  the  same  thing  as  the 
subject  itself  In  the  one  case,  the  subject  rejects  a  sugges- 
tion through  a  quality  of  its  own,  in  the  other  it  may  reject 
on  the  strength  of  our  failure.  But  I  must  persist  in  denying 
that  this  objection  is  relevant.  In  both  cases  alike  the  subject 
is  taken  as  somehow  determined  ;  and  it  is  this  determination 
which  (whatever  it  comes  from)  does  give  the  subject  a 
positive  character,  which  in  both  cases  lies  at  the  base  of  the 
denial.  No  subject  could  repel  an  offered  suggestion  simply 
on  the  strength  of  what  it  was  not.  It  is  because  the 
"not-this"  must  mean  "something  else^'  that  we  are  able 
to  make  absence  a  ground  for  denial.  We  shall  all  agree 
that  the  nothing  which  is  nothing  can  not  possibly  do 
anything,  or  be  a  reason  for  aught. 

These  distinctions  do  not  touch  the  principle  we  stand 
upon,  but  I  admit  they  give  rise  to  most  serious  difficulties. 
And,  mainly  for  the  sake  of  future  chapters,  it  may  be  well  if 
we  attempt  here  to  clear  our  ideas.  And  (i)  first,  when  we 
have  a  case  of  "  opposition,"  there  the  subject  repels  the  offered 
predicate  because  it  has  in  its  content  a  positive  quality, 
filling  the  space  which  the  predicate  would  occupy,  and  so 
expelling  it.  If  a  man  has  blue  eyes,  then  that  quality  of 
blueness  is  incompatible  with  the  quality  brown.  But  (ii), 
when  we  come  to  privation,  two  cases  are  possible.  In  the 
first  of  these  {a)  within  the  content  of  the  subject  there  is 
empty  space  where  a  quality  should  be.  Thus,  a  man  being 
eyeless,  in  this  actual  content  lies  the  place  where  his  eyes 
would  be  if  he  had  them.  And  this  void  can  not  possibly  be 
a  literal  blank.  You  must  represent  the  orbits  as  somehow 
occupied,  by  peaceful  eyelids,  or  unnatural  appearance.  And 
so  the  content  itself  gets  a  quality,  which,  in  contrast  to  the 

I 


114  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

presence  of  eyes,  may  be  nothing,*  but  which  by  itself,  has  a 
positive  character,  which  serves  to  repel  the  suggestion  of  sight. 

§  ID.  But  privation  can  rest  on  another  basis  {b).  The 
content  of  the  subject  may  contain  no  space  which  could 
possibly  be  qualified  by  the  presence  of  the  predicate.  What 
rejects  the  predicate  is  no  other  determination  of  the  con- 
tent itself,  but  is,  so  far  as  that  content  itself  is  concerned, 
an  absolute  blank.  It  is  difficult  to  find  illustrations  of 
this  instance.  If  I  say  "A  stone  does  not  feel  or  see,"  it 
may  rightly  be  urged  "Yes,  because  it  is  a  stone,  and  not 
simply  because  it  is  nothing  else."  But  we  can  find  an 
example  of  the  privation  we  want  in  the  abstract  universal. 
The  universal  idea  (cf  Sigwart,  130),  if  you  keep  it  in  abstrac- 
tion, repels  every  possible  extension  of  its  character.  Thus 
"  triangle,"  if  you  mean  by  it  the  mere  abstraction,  can  neither 
be  isosceles  nor  scalene  nor  rectangular;  for,  if  it  were,  it 
would  cease  to  be  undetermined.  We  may  invent  a  stupid 
reductio  ad  absurdum  :  This  isosceles  figure  is  certainly  a 
triangle,  but  a  triangle  is  certainly  not  isosceles,  therefore . 

If  we  release  the  universal  from  this  unnatural  abstraction, 
and  use  it  as  an  attribute  of  real  existence,  then  it  can  not  support 
such  a  privative  judgment.  For,  when  referred  to  reality,  we 
know  it  must  be  qualified,  though  we  perhaps  can  not  state 
its  qualification.  Once  predicate  triangle  of  any  figure,  and 
we  no  longer  can  deny  every  other  quality.  The  triangle  is 
determinate,  though  we  are  not  able  to  say  how.  It  is  only 
the  triangle  as  we  happen  not  to  know  it,  which  repels  the 
suggestion  of  offered  predicates.  It  is  our  ignorance,  in 
short,  and  not  the  idea,  which  supports  our  exclusion  of  every 
suggestion. 

§  II.  In  a  judgment  of  this  kind  the  base  of  denial  is 
neither  the  content  of  the  subject  itself,  nor  is  it  that  content 
plus  a  simple  absence  ;  for  a  simple  absence  is  nothing  at  all. 

*  I  may  mention  that,  though  contrast  can  not  always  be  taken  as 
holding  true  of  the  things  contrasted,  yet  for  all  that  it  may  rest  on  a 
positive  quality.  Thus,  even  in  the  case  of  a  word  like  bhndness,  we 
should  be  wrong  if  we  assumed  that  the  blind  man  is  qualified  simply  by 
the  absence  of  sight  from  the  part  which  should  furnish  vision.  His  mind, 
we  can  not  doubt,  has  a  positive  character  which  it  would  lose  if  another 
sense  were  added. 


Chap.  III.]  THE   NEGATIVE  JUDGMENT.  II5 

The  genuine  subject  is  the  content  of  the  \dedi.  plus  ;;^j  psycho- 
logical state  of  mind.  The  universal  abstraction,  ostensibly 
unqualified,  is  determined  by  my  mental  repulsion  of  qualities. 
And  the  positive  area  which  excludes  the  predicate  really  lies 
in  that  mental  condition  of  mine.  My  ignorance,  or  again  my 
wilful  abstraction,  is  never  a  bare  defect  of  knowledge.  It  is 
a  positive  psychological  state.  And  it  is  by  virtue  of  relation 
to  this  state,  which  is  used  as  content  to  qualify  the  subject, 
that  the  abstraction,  or  the  ignorance,  is  able  to  become  a 
subject  of  privation.  We  shall  see  that,  in  this  form,  the 
universal  may  more  truly  be  called  particular  (Chap.  VI.  §  35)  ; 
for  it  is  determined  and  qualified,  not  by  any  developement  of 
the  content,  but  simply  by  extraneous  psychological  relation. 

§  12.  The  various  kinds  of  negative  judgment  follow 
closely  the  varieties  of  affirmation.  The  immediate  subject 
may  be  part  of  the  content  of  present  perception  ("  This  stone 
is  not  wet "  )  ;  or  it  may  be  found  in  some  part  of  the  series  of 
space,  or  again  of  time,  which  we  do  not  perceive  ("  Marseilles 
is  not  the  capital  of  France,"  "  It  did  not  freeze  last  night "). 
Again  what  is  denied  may  be  a  general  connection  ("  A  metal 
need  not  be  heavier  than  water ").  In  this  last  case  it  is  of 
course  the  unexpressed  quality  at  the  base  of  the  hypothesis 
(Chap.  II.  §  50)  which  the  real  excludes.  But,  in  all  negative 
judgment,  the  ultimate  subject  is  the  reality  that  comes  to  us 
in  presentation.  We  affirm  in  all  alike  that  the  quality  of 
the  real  excludes  an  ideal  content  that  is  offered.  And  so 
every  judgment,  positive  or  negative,  is  in  the  end  existential. 

In  existential  judgment,  as  we  saw  before  (Chap.  II.  §  42), 
the  apparent  is  not  the  actual  subject.  Let  us  take  such  a 
denial  as  "  Chimaeras  are  non-existent."  "  Chimaeras "  is 
here  ostensibly  the  subject,  but  is  really  the  predicate.  It  is 
the  quality  of  harbouring  chimaeras  which  is  denied  of  the 
nature  of  things.  And  we  deny  this  because,  if  chimaeras 
existed,  we  should  have  to  alter  our  view  of  the  world.  In 
some  cases  that  view,  no  doubt,  can  be  altered,  but,  so  long  as 
we  hold  it,  we  are  bound  to  refuse  all  predicates  it  excludes. 
The  positive  quality  of  the  ultimate  reality  may  remain  occult 
or  be  made  explicit,  but  this,  and  nothing  else,  lies  always  at 
the'  base  of  a  negative  judgment. 

I  2 


Il6  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

§  1 3.  For  logical  negation  can  not  be  so  directly  related  to 
fact  as  is  logical  assertion.  We  might  say  that,  as  such  and 
in  its  own  strict  character,  it  is  simply  "subjective  : "  it  does 
not  hold  good  outside  my  thinking.  The  reality  repels  the 
suggested  alteration  ;  but  the  suggestion  is  not  any  movement 
of  the  fact,  nor  in  fact  does  the  given  subject  maintain  itself 
against  the  actual  attack  of  a  disparate  quality.  The  process 
takes  place  in  the  unsubstantial  region  of  ideal  experiment. 
And  the  steps  of  that  experiment  are  not  even  asserted  to 
exist  in  the  world  outside  our  heads.  The  result  remains,  and 
is  true  of  the  real,  but  its  truth,  as  we  have  seen,  is  something 
other  than  its  first  appearance. 

The  reality  is  determined  by  negative  judgments,  but  it 
can  not  be  said  to  be  directly  determined.  The  exclusion,  as 
such,  can  not  be  ascribed  to  it,  and  hence  a  variety  of  ex- 
clusions may  be  based  on  one  single  quality.  The  soul  is  not 
an  elephant,  nor  a  ship  in  full  sail,  nor  a  colour,  nor  a  fire- 
shovel  ;  and,  in  all  these  negations,  we  do  make  an  assertion 
about  the  soul.  But  you  can  hardly  say  that  the  subject  is 
determined  by  these  exclusions  as  such,  unless  you  will 
maintain  that,  after  the  first,  the  remainder  must  yield  some 
fresh  piece  of  knowledge.  You  may  hold  that  "  all  negation 
is  determination,"  if  you  are  prepared  to  argue  that,  in  the 
rejection  of  each  new  absurd  suggestion,  the  soul  exhibits  a 
fresh  side  of  its  being,  and  in  each  case  performs  the  special 
exclusion  by  means  of  a  new  quality.  But  it  seems  better  to 
say  that  nothing  is  added  by  additional  exclusions.  The  deve- 
lopement  and  application  of  these  may  proceed  ad  infinitum^ 
but  the  process  is  arbitrary  and,  in  the  end,  unreal.  The  same 
quality  of  the  soul  which  repels  one  predicate,  repels  here  all 
the  rest,  and  the  exclusion  itself  takes  place  only  in  our  heads. 

I  do  not  mean  to  deny  that  a  thing  may  be  qualified  by 
the  exclusion  of  others,  that  the  real  character  of  a  fact  may 
depend  on  what  may  be  called  a  negative  relation.  What  I 
mean  to  say  is  that  the  negative  judgment  will  not  express 
this.  It  asserts  that  a  predicate  is  incompatible,  but  it  does 
not  say  that  either  the  predicate,  or  the 'incompatibility,  are 
real  facts.  If  you  wish  to  say  this  you  must  transcend  the 
sphere  of  the  negative  judgment. 


Chap.  III.]  THE   NEGATIVE  JUDGMENT.  1 1  / 

§  14.  We  must  not,  if  we  can  help  it,  introduce  into  logic 
the  problems  of  the  "  dialectical  "  view.  It  may  be,  after  all, 
that  everything  is  just  so  far  as  it  is  not,  and  again  is  not  just 
so  far  as  it  is.  Everything  is  determined  by  all  negation  ;  for  it 
is  what  it  is  as  a  member  of  the  whole,  and  its  relation  to  all 
other  members  is  negative.  Each  element  in  the  whole,  itself 
the  whole  ideally  while  actually  finite,  transcends  itself  by 
mere  self-assertion,  and  by  mere  self-emphasis  brings  forth  the 
other  that  characterizes  and  negates  it.  If  everything  thus 
has  its  disparate  in  itself,  then  everything  in  a  sense  must  be 
its  own  discrepancy.  Negation  is  not  only  one  side  of  reality, 
but  in  the  end  it  is  either  side  we  please.  On  this  view  it 
would  be  doubtful  if  even  the  whole  is  positive  ;  for  it  is  just 
so  far  as  by  position  it  disperses  itself  in  its  own  negation,  and 
begets  from  its  dispersion  the  opposite  extreme.  It  is  doubt- 
ful if  we  may  not  transform  the  saying  that  "  Everything  is 
nothing  except  by  position,"  into  "  Everything  by  position 
is  its  proper  contrary,  and  nothing  by  position  is  all  and 
everything." 

If  this  is  so,  there  would  remain  no  quality  which  is 
simply  positive ;  and  logical  negation,  in  another  sense  than 
we  have  given  it  above,  becomes  the  soul  and,  we  sometimes 
are  inclined  to  think,  the  body  of  the  real  world.  But  we  are 
not  called  upon  to  discuss  this  view  (cf.  Chap.  V.),  for  our 
result  will  stand  in  any  case,  I  think,  in  its  principal  outline. 

A  mere  logical  negation,  it  is  fully  admitted  by  the 
dialectical  method,  need  not  express  a  real  relation.  And, 
this  being  so,  it  seems  the  better  course  to  consider  it  by  itself 
as  merely  subjective,  and  to  express  the  real  implication  of 
exclusives  by  an  affirmative  judgment,  which  sets  forth  that 
fact.  ( What  denial  tells  us  is  merely  this,  that,  when  we  bring 
the  disparate  up,  it  is  rejected.  Whether  what  repels  it  is 
entirely  independent,  or  whether  it  has  itself  produced  or 
solicited  what  it  excludes,  is  quite  irrelevant.  )  And  it  is  still 
more  irrelevant  to  ask  the  question  if  the  first  rejection  is 
merely  coquettish,  and  will  lead  in  the  end  to  a  deeper 
surrender.  This  all  goes  beyond  what  denial  expresses,  for 
that,  merely  by  itself,  is  not  asserted  beyond  our  minds. 

The  dialectical  method,  in  its  unmodified  form,   may  be 


Il8  THE  PRINCIPLES   OF   LOGIC.  [Book  L 

untenable.  It  has,  however,  made  a  serious  attempt  to  deal 
with  the  relation  of  thought  to  reality.  We  can  hardly  say 
that  of  those  eminent  writers  who  are  sure  that  logic  is  the 
counterpart  of  things,  and  have  never  so  much  as  asked  them- 
selves the  question,  if  the  difference  and  identity,  with  which 
logic  operates,  are  existing  relations  between  actual  phenomena. 

§  15.  To  resume,  logical  negation  always  contradicts,  but 
never  asserts  the  existence  of  the  contradictory.  To  say 
"  A  is  not  B  "  is  merely  the  same  as  to  deny  that  "  A  is  B,"  or 
to  assert  that  "  A  is  B  "  is  false.  And,  since  it  can  not  go  beyond 
this  result,  a  mere  denial  of  B  can  never  assert  that  the  con- 
tradictory Not-B  is  real.  The  fact  it  does  assert  is  the 
existence  of  an  opposite  incompatible  quality,*  either  in  the 
immediate  or  ultimate  subject.  This  is  the  reason  why  the 
suggested  A  —  B  is  contradicted  ;  and  it  is  only  because  this 
something  else  is  true,  that  the  statement  A  — B  is  rejected 
as  false.  But  then  this  positive  ground,  which  is  the  basis  of 
negation,  is  not  contradictory.  It  is  merely  disparate,  opposite, 
incompatible.  It  is  only  contrary.  In  logical  negation  the 
denial  and  the  fact  can  never  be  the  same. 

§  16.  The  contradictory  idea,  if  we  take  it  in  a  merely 
negative  form,  must  be  banished  from  logic.  If  Not-A 
were  solely  the  negation  of  A,  it  would  be  an  assertion  with- 
out a  quality,  and  would  be  a  denial  without  anything  positive 
to  serve  as  its  ground.  A  something  that  is  only  not  some- 
thing else,  is  a  relation  that  terminates  in  an  impalpable  void, 
a  reflection  thrown  upon  empty  space.  It  is  a  mere  nonentity 
which  can  not  be  real.  And,  if  such  were  the  sense  of  the 
dialectical  method  (as  it  must  be  confessed  its  detractors 
have  had  much  cause  to  suppose),  that  sense  would,  strictly 
speaking,  be  nonsense.  It  is  impossible  for  anything  to  be 
07tly  Not-A.  It  is  impossible  to  realize  Not-A  in  thought. 
It  is  less  than  nothing,  for  nothing  itself  is  not  wholly  negative. 
Nothing  at  least  is  empty  thought,  and  that  means  at  least  my 
thinking  emptily.  Nothing  means  nothing  else  but  failure. 
And  failure  is  impossible  unless  something  fails  :  but  Not-A 
would  be  impersonal  failure  itself  (§  11). 

Not-A  must  be  more  than  a  bare  negation.  It  must 
\  *  On  the  nature  of  incompatibility  see  more,  Chap.  V. 


Chap.  III.]  THE   NEGATIVE  JUDGMENT.  II 9 

also  be  positive.  It  is  a  general  name  for  any  quality  which, 
when  you  make  it  a  predicate  of  A,  or  joint  predicate  with  A, 
removes  A  from  existence.  The  contradictory  idea  is  the 
universal  idea  of  the  discrepant  or  contrary.  In  this  form  it 
must  keep  its  place  in  logic.  It  is  a  general  name  for  any 
hypothetical  disparate ;  but  we  must  never  for  a  moment 
allow  ourselves  to  think  of  it  as  the  collection  of  disparates. 

§  17.  Denial  or  contradiction  is  not  the  same  thing  as 
the  assertion  of  the  contrary  ;  but  in  the  end  it  can  rest  on 
nothing  else.  The  contrary  however  which  denial  asserts, 
is  never  explicit.  In  "  A  is  not  B  "  the  disparate  ground  is 
wholly  unspecified.  The  basis  of  contradiction  may  be  the 
assertion  A-C  or  A-D,  C  and  D  being  contraries  of  B. 
But  again  it  may  perhaps  be  nothing  of  the  sort.  We  may 
reject  A-B,  not  in  the  least  on  the  ground  of  A,  but  because 
A  itself  is  excluded  from  reality.  The  ultimate  real  may 
be  the  subject  which  has  some  quality  disparate  with  A-B. 
For  contradiction  rests  on  an  undetermined  contrary.  It  does 
not  tell  us  what  quality  of  the  subject  excludes  the  predicate. 
It  leaves  us  in  doubt  if  the  subject  itself  is  not  excluded. 
Something  there  is  which  repels  the  suggestion  ;  and  that  is 
all  we  know.  Sokrates  may  be  not  sick  because  he  is  well,  or 
because  there  is  now  no  such  thing  as  Sokrates. 

§  18.  Between  acceptance  and  rejection  there  is  no  middle- 
point,  and  so  contradiction  is  always  dual.  There  is  but  one 
Not-B.  But  contrary  opposition  is  indefinitely  plural.  The 
number  of  qualities  that  are  disparate  or  incompatible  with  A, 
can  not  be  determined  by  a  general  rule.  It  is  possible  of 
course  to  define  a  contrary  in  some  sense  which  will  limit  the 
use  of  the  term ;  but  for  logical  purposes  this  customary 
restriction  is  nothing  but  lumber.  In  logic  the  contrary 
should  be  simply  the  disparate.  Nothing  is  gained  by  trying 
to  keep  up  an  effete  tradition.  If  a  technical  distinction 
can  not  be  called  necessary,  it  is  better  to  have  done  with  it. 

§  19.  Contradiction  is  thus  a  "subjective"  process,  which 
rests  on  an  unnamed  disparate  quality.  It  can  not  claim 
"objective"  reality;  and  since  its  base  is  undetermined,  it  is 
hopelessly  involved  in  ambiguity.  In  "  A  is  not  B  "  you  know 
indeed  what  it  is  you  deny,  but  you  do  not  say  what  it  is  you 


1 20  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

affirm.  It  may  be  a  quality  in  the  nature  of  things  which  is 
incompatible  with  A,  or  again  with  B.  Or  again  it  may  be 
either  a  general  character  of  A  itself  which  makes  B  im- 
possible, or  it  may  be  some  particular  predicate  C.  That 
"  a  round  square  is  three-cornered,"  or  that  "  happiness  lies  in 
an  infinite  quantity,"  may  at  once  be  denied.  We  know  a 
round  square,  or  an  infinite  number,  are  not  in  accordance 
with  the  nature  of  things.  But  "  virtue  is  quadrangular,"  or 
"  is  mere  self-seeking,"  we  deny  again  because  virtue  has  no 
existence  in  space,  and  has  another  quality  which  is  opposite 
to  selfishness. 

"  The  King  of  Utopia  did  ^^^  die  on  Tuesday "  may  be 
safely  contradicted.  And  yet  the  denial  must  remain  am- 
biguous. The  ground  may  be  that  there  is  no  such  place, 
or  it  never  had  a  king,  or  he  still  is  living,  or,  though  he  is 
dead,  yet  he  died  on  Monday.  This  doubtful  character  can 
never  be  removed  from  the  contradiction.  It  is  the  rejection 
of  an  idea,  on  account  of  some  side  of  real  fact  which  is 
implied  but  occult. 

§  20.  We  may  conclude  this  chapter  by  setting  before 
ourselves  a  useful  rule.  I  think  most  of  us  know  that  one 
can  not  afiirm  without  also  in  effect  denying  something.  In  a 
complex  universe  the  predicate  you  assert  is  certain  to  exclude 
some  other  quality,  and  this  you  may  fairly  be  taken  to  deny. 
But  another  pitfall,  if  not  so  open,  yet  no  less  real,  I  think 
that  some  of  us  are  quite  unaware  of.  Our  sober  thinkers, 
our  discreet  Agnostics,  our  difiident  admirers  of  the  phenomenal 
region — I  wonder  if  ever  any  of  them  see  how  they  com- 
promise themselves  with  that  little  word  "  onlyr  How  is  it 
that  they  dream  there  is  something  else  underneath  appearance, 
and  first  suspect  that  what  meets  the  eye  veils  something 
hidden  ?  But  our  survey  of  negation  has  taught  us  the  secret, 
that^othing  in  the  world  can  ever  be  denied  except  on  the 
strength  of  positive  knowledge.  I  hardly  know  if  I  am  right 
in  introducing  suggestive  ideas  into  simple  minds  ;  but  yet  I 
must  end  with  the  rule  I  spoke  of  We  can  not  deny  without 
also  affirming  ;  and  it  is  of  the  very  last  importance,  whenever 
we  deny,  to  get  as  clear  an  idea  as  we  can  of  the  positive 
ground  our  denial  rests  on. 


(       121       ) 


CHAPTER  IV. 

THE   DISJUNCTIVE  JUDGMENT. 

§  I.  The  vdisjunctive  judgment  may  fairly  complain  that 
by  most  logicians  it  is  hardly  dealt  with.  It  is  often  taken 
as  a  simple  application  of  the  hypothetical,  and  receives  the 
treatment  of  a  mere  appendage.  It  is  wonderful  in  how  many 
respectable  treatises  not  the  smallest  attempt  is  made  to 
understand  the  meanings  of  "if"  and  of  "either — or." 

The  commonest  way  of  regarding  disjunction  is  to  take  it 
as  a  combination  of  hypotheses.  This  view  in  itself  is  some- 
what superficial,  and  it  is  possible  even  to  state  it  incorrectly. 
"  Either  A  is  B  or  C  is  D  "  means,  we  are  told,  that  if  A  is 
not  B  then  C  is  D,  and  if  C  is  not  D  then  A  is  B.  But  a 
moment's  reflection  shows  us  that  here  two  cases  are  omitted. 
Supposing,  in  the  one  case,  that  A  is  B,  and  supposiag,  in  the 
other,  that  C  is  D,  are  we  able  in  these  cases  to  say  nothing 
at  all  .^  Our  "  either — or  "  can  certainly  assure  us  that,  if  A  is 
B,  C-D  must  be  false,  and  that,  if  C  is  D,  then  A-B  is 
false.  We  liave  not  exhausted  the  disjunctive  statement, 
until  we  have  provided  for  four  possibilities,  B  and  not-B, 
C  and  not-C. 

§  2.  But  however  complete  may  be  the  cases  supposed, 
disjunctive  judgments  can  not  really  be  reduced  to  hypothe- 
ticals.  Their  meaning,  no  doubt,  can  be  given  hypothetically  ; 
but  we  must  not  go  on  to  argue  from  this  that  they  are 
hypothetical.  The  man  who  illustrated  everything  else  has 
touched  this  point  too  in  the  Gentlemen  of  Verona  : 

Speed.    But  tell  me  true,  will't  be  a  match  ? 

Lau?ice.  Ask  my  dog  :  if  he  say,  ay,  it  will ;  if  he  say,  no,  it  will ;  if 
he  shake  his  tail  and  say  nothing,  it  will. 

Speed.     The  conclusion  is  then  that  it  will. 

Launce.  Thou  shalt  never  get  such  a  secret  from  me  but  by  a 
parable  (Act  II.  Scene  v.). 


122  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

It  is  indeed  by  an  indirect  process,  and  by  making  secret 
a  categorical  judgment,  that  hypothetical  can  express  dis- 
junction. 

I  do  not  mean  that  the  "  either — or  "  is  purely  categorical. 
I  mean  that  to  some  extent  at  least  it  is  categorical,  and 
declares  a  fact  without  any  supposition.  In  "A  is  b  or  ^ " 
some  part  of  the  statement  is  quite  unconditional.  It  asserts 
a  fact  without  any  "  if "  at  all.  And  when  pressed  with  the 
objection,  "  But  you  can  not  deny  that  it  is  reduced  to  a 
combination  of  supposals,"  we  need  not  take  long  to  practise 
an  answer.  A  combination  of  hypothetical  surely  does  not 
lie  in  the  hypothetical  themselves.  It  lies  in  the  mind 
which  combines  them  together,  and  surveys  the  field  which 
together  they  exhaust.  It  is  nonsense  to  say  you  are  able 
to  "  reduce  "  a  statement  to  elements  of  a  certain  character, 
when  these  elements,  if  taken  merely  by  themselves  and 
without  a  peculiar  mode  of  union,  are  able  to  express  nothing 
like  the  statement.  The  basis  of  disjunction,  the  ground  and 
foundation  of  your  hypothetical,  is  categorical. 

§  3.  There  is,  no  doubt,  ^ome  difficulty  about  the  catego- 
rical nature  of  disjunctive  judgments.  "A  is  b  ox  c  ;''  but  this 
mode  of  Speech  can  not  possibly  answer  to  real  fact.  No  real 
fact  can  be  "  either — or."  It  is  both  or  one,  and  between  the 
two  there  is  nothing  actual.  We  can  hardly  mean  to  say  that 
in  fact  A  is  b  or  c.  On  the  other  hand,  we  are  far  from 
expressing  simple  ignorance.  If  we  merely  said  "  I  do  not 
know  if  A  is  ^,  and  I  do  not  know  if  A  is  ^,"  that  would  not 
be  equivalent  to  the  original  statement.  And  that  we  make 
an  assertion  can  be  shown  in  this  way.  If  the  subject  of  our 
predicate  "  either — or  "  were  proved  not  to  exist,  our  statement 
would  be  false.  It  is  clear  not  only  that  the  subject  has 
existence,  but  that  it  also  possesses  some  further  quality. 

The  distinction  of  the  apparent  and  the  ultimate  subject, 
which  we  had  to  make  in  our  former  discussions,  must  not 
here  be  forgotten.  "A  is  either  b  or  c''  need  not  always 
imply  that  A  is  a  fact.  For  example,  I  may  say  that 
"either  A  exists  or  does  not  exist."  The  subject  here  is  the 
nature  of  things,  and  this  either  repels  the  content  A  or  is 
qualified  by  it.     But  still  the  assertion  remains  categorical. 


Chap.  IV.]  THE   DISJUNCTIVE  JUDGMENT.  1 23 

Throughout  the  rest  of  the  chapter  I  shall  take  A  to  stand  for 
the  real  subject,  and  the  reader  must  remember  that  in  every 
case  the  apparent  subject  may  belong  to  the  predicate,  and 
that  what  is  asserted  respecting  A  may  only  be  true  of  the 
ultimate  subject. 

And  the  same  remark  applies  to  such  examples  as 
"  Either  A  is  B  or  C  is  D."  The  subject  in  this  case  is  not 
A  or  B  or  again  C  or  D.  The  subject  is  jhe  real,  which 
is  qualified  either  by  the  predicate  A-B  or  the  predicate 
C-D. 

§  4.  The  assertion  in  "  A  is  <^  or  ^  "  is  not  that  A  is  b  or  c. 
What  then  do  we  affirm  ?  We  say  in  the  first  place  that  A 
exists.  In  the  next  place  we  certainly  give  it  some  quality. 
What  quality  do  we  give  it }  If  it  can  not  be  either  b  or  c, 
can  it  possibly  be  something  that  falls  between  them  .?  No, 
for  that  would  be  neither.  For  instance,  grey  is  not  white  or 
black,  and  it  excludes  both  colours.  The  predicate  of  A,  while 
neither  b  nor  ^,  must  not  be  a  quality  exclusive  of  either.  It 
must  then  be  a  quality  common  to  both,  which  is  not  yet 
either,  but  is  further  determinable  as  one  or  the  other. 

§  5.  If  we  like  to  call  this  basis  x^  then  "A  is  .r  "is  catego- 
rically true.  We  may  in  some  cases  have  distinguished  x 
and  given  it  a  name,  but  in  other  cases  it  is  unnamed  and 
implicit.  "  Man,  woman,  and  child,"  have  a  common  basis  in 
"  human  being."  In  "  white  or  black  "  the  quality  "  coloured, 
and  coloured  so  as  to  exclude  other  hues,"  is  the  attribute 
asserted.  "  In  England  or  America,"  "  alive  or  dead,"  commit 
us  to  the  statements  "somewhere  not  elsewhere"  and  "or- 
ganized being."  And  so,  if  we  call  a  man  "  bad  or  good,"  we 
say  at  least  he  is  a  moral  agent.  There  is  no  exception  to 
the  truth  of  this  rule.  Even  existence  and  non-existence 
have  so  much  in  common  that,  in  any  sense  in  which  we 
can  use  them,  they  imply  some  kind  of  contact  with  my 
mind.  We  have  seen  (Chap.  III.)  that  there  is  no  pure 
negation.  So,  in  every  disjunction  and  as  the  ground  of  it, 
there  must  be  the  assertion  of  a  common  quality,  the  sphere 
within  which  the  disjunction  is  affirmed. 

§  6.  But  X  is  not  any  universal  whatever  which  happens 
to  be  common  to  b  and  c.     It  is  particularized  further.     It 


1 24  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

excludes  the  opposite  of  each  of  these  qualities,  and  can  not  be 
the  negative  of  "  b  or  ^."  It  is  affirmed  as  fully  determined  not 
outside  the  region  which  is  covered  by  be.  But  since  b  and  c, 
as  predicates  of  A,  are  incompatible,  it  can  not  be  both  of 
them.  The  conclusion  remains  that  it  must  be  one.  "One 
single  element  of  the  region  enclosed  by  be  "  is  the  predicate 
common  to  b  and  c.  And  this  predicate  it  is  which,  in  dis- 
junction, we  categorically  assert  of  A. 

So  much  is  "fact  and  no  hypothesis ;  but  this  by  itself 
would  not  be  the  assertion  ''^bor  e!'  The  disjunctive  judgment 
is  not  wholly  categoric.  Being  sure  of  our  basis,  the  quality 
X,  upon  this  universal  we  erect  hypotheses.  We  know  that 
b  and  c  are  disparate.  We  know  that  A  is  particularized 
within  b  and  c,  and  therefore  as  one  of  b  and  e.  It  can  not  be 
both,  and  it  must  be  some  one.  So  much  is  the  fact.  To 
complete  the  disjunction  we  add  the  supposal,  "  If  it  is  not  one 
it  must  be  the  other."  If  A  is  not  ^,  it  must  be  c  ;  and  it  must 
be  ^,  if  it  is  not  e.  This  supposal  completes  the  "  either — or." 
Disjunctive  judgment  is  the  union  of  hypothetical  on  a 
categoric  basis. 

§  7.  We  shall  return  to  consider  this  process  further,  but 
at  present  we  may  pause  to  correct  a  mistake.  It  has  been 
doubted  if  alternatives  are  always  exclusive.  "  A  is  <^  or  r,"  it 
is  said,  may  be  taken  to  admit  that  A  is  possibly  both.  It 
may  either  be  be  or  b  or  e.  And,  no  doubt,  in  our  ordinary 
disjunctive  statements  we  either  leave  the  meaning  to  be 
gathered  from  the  context,  or  really  may  not  know  what  it  is 
that  we  mean.  But  our  slovenly  habits  of  expression  and 
thought  are  no  real  evidence  against  the  exclusive  character 
of  disjunction.  "  A  is  <^  or  ^"  does  strictly  exclude  "A  is  both 
b  and  ^."  When  a  speaker  asserts  that  a  given  person  is  a  fool 
or  a  rogue,  he  may  not  mean  to  deny  that  he  is  both.  But, 
having  no  interest  in  showing  that  he  is  both,  being  perfectly 
satisfied  provided  he  is  one,  either  b  or  e,  the  speaker  has  not 
the  possibility  be  in  his  mind.  Ignoring  it  as  irrelevant,  he 
argues  as  if  it  did  not  exist.  And  thus  he  may  practically  be 
right  in  what  he  says,  though  formally  his  statement  is  down- 
right false  :  for  he  has  excluded  the  alternative  be. 

And  it  is  not  always  safe  to  be  slovenly.     It  may  be  a 


Chap.  IV.]  THE   DISJUNCTIVE  JUDGMENT.  1 25 

matter  of  vital  moment  to  make  our  disjunction  accurate  and 
complete,  and  to  know  if  we  mean  "  A  is  ^  or  ^,"  or  "A  is  be  or 
b  or  cr  About  the  commonest  mistake  in  metaphysics  is  the 
setting  up  of  false  alternatives.  If  we  either  admit  be  as  a 
predicate  when  b  and  c  are  disparate,  or  exclude  be  when  b 
and  e  are  compatible,  we  are  liable  to  come  to  most  false 
conclusions.  And  the  very  instance  we  have  quoted  above 
should  read  us  a  lesson.  It  is  false  that  the  alternative 
"  either  rogue  or  fool "  does  never  exclude  the  possibility  of 
both.  It  is  a  common  thing  to  make  this  mistake.  When 
we  try  to  guess  a  man's  line  of  conduct,  we  first  lay  it  down  he 
is  fool  or  rogue,  and  then  afterwards,  arguing  that  he  is  certainly 
a  rogue,  we  conclude  that  his  conduct  will  be  deliberately  sel- 
fish. But  unfortunately  the  man  has  been  a  fool  as  well,  and 
was  not  in  any  way  to  be  relied  on.  It  is  often  impossible  to 
speak  by  the  card,  but  still  inaccuracy  remains  inaccuracy. 
And,  if  we  do  not  mention  the  alternative  "  or  both,"  when  held 
to  our  words  we  certainly  exclude  it. 

If  we  mean  to  say  "  A  is  ^  or  <:  or  again  bc^'  the  process 
of  the  judgment  is  very  simple.  A  exists  and  is  further 
determined.  It  is  determined  within  the  region  be.  A  ex- 
cludes all  qualities  which  are  incompatible  with  b  and  e  and 
again  with  be.  Within  be  fall  b  and  e  and  again  be,  and 
nothing  else  falls  there.  And  since  these  are  disparate, 
A  is  but  one  of  them.  So  far  the  fact,  and  then  come 
the  hypotheses.  If  A  as  determined  excludes  b  and  e  it 
must  be  be :  if  it  excludes  e  and  be  it  is  b :  if  it  excludes  b  and 
be  it  is  e.  The  number  of  disparates  is  of  course  irrelevant  to 
the  nature  of  the  process. 

§  8.  But  the  inaccuracy  we  have  noticed  has  a  natural 
foundation.  We  are  accustomed  to  use  "  or  "  with  an  impli- 
cation, and  at  times  we  forget  whether  "  or  "  stands  alone  or 
must  be  taken  as  so  qualified.  I  will  briefly  illustrate.  If,  in 
drawing  up  a  rule,  I  lay  down  that  "  the  number  of  tickets 
being  limited,  each  person  shall  be  entitled  to  a  red  ticket  or 
a  white  one,"  it  is  at  once  understood  that  the  alternatives  are 
incompatible.  A  ticket  means  here  obviously  one  at  most. 
But,  if  I  say  "  No  one  shall  be  entitled  to  pass  within  this 
enclosure  except  the  possessor  of  a  white  or  red  ticket,"  I 


1 26  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

should  hardly  be  taken  to  exclude  the  man  who  was  qualified 
by  both.  A  ticket  means  here  one  at  least.  And  it  becomes 
very  easy  to  misunderstand,  and  to  suppose  that  "  or  "  in  each 
of  these  cases  has  a  different  force. 

But  in  both  cases  "  or  "  means  precisely  the  same.  In  the 
second,  as  in  the  first,  it  is  rigidly  disjunctive.  But  in  the 
second  of  our  instances  "or"  does  not  stand  alone.  It  is 
qualified  by  an  unexpressed  "  if  not "  or  "  failing  that."  And 
this  implication  makes  a  vital  difference. 

§  9.  The  alternatives  which  are  offered  are  not  red  and 
white.  I  am  not  to  be  admitted,  given  white  or  red.  The 
entitling  conditions  (so  far  as  they  are  contemplated)  are  firstly 
''  white,"  and  then  "  red,  white  failing  "  or  "  red  without  white  ; " 
and  it  can  hardly  be  maintained  that  these  conditions  are 
compatible.  For,  if  white  is  there,  then  red  can  not  make 
good  the  failure  of  white,  and  the  red,  that  is  specified  as 
excluding  white,  can  not  by  any  means  admit  its  presence. 
What  you  mean  to  say  is,  Suppose  white  is  there,  then  cadit 
qucestio ;  but,  if  white  is  not  there,  red  will  answer  the 
purpose.  And  you  express  your  meaning  by  assigning  two 
alternatives,  "white  present"  on  the  one  hand,  and,  on  the 
other  hand,  "  red  coupled  with  the  absence  of  white."  And 
this  practically  provides  for  every  possibility. 

The  logical  objection  which  may  be  raised  against  it  is  not 
that  its  "or"  is  partly  conjunctive,  for  this,  as  we  have  seen,  is 
a  pure  mistake.  The  disjunction  is  faulty  not  because  it  is 
conjunctive,  but  because  it  is  incomplete.  It  ignores  the 
possibility  of  the  co- existence  of  red  and  white,  and  in  form  it 
might  be  construed  as  excluding  it.  But  the  reason  is 
obvious.  You  are  never  forced  to  consider  separately  this 
individual  possibility,  since  you  can  always  treat  it  as  a 
simple  case  of  the  presence  of  white.  If  "  white  "  really  means 
"  white  with  or  without  red,"  and  "  red  "  means  "  red  on  the 
failure  of  white,"  and  if  the  absence  of  both  is  fully  provided 
for,  then  the  disjunction  is  absolutely  complete  and  ex- 
haustive. And  these  alternatives  (i)  white  with  or  without 
red,  (ii)  red  without  white,  and  (iii)  failure  of  both,  are 
absolutely  incompatible. 

§  10.  And   this   I  think  is   the   answer   to   an    argument 


Chap.  IV.]  THE   DISJUNCTIVE  JUDGMENT.  12/ 

brought  forward  by  Professor  Jevons  (Principles^  p.  73). 
Against  the  exclusive  character  of  alternatives  he  urges  an 
indirect  argument.  If  that  were  so,  he  objects,  the  negative 
of  such  a  term  as  "  malleable-dense-metal  "  could  not  be  "  not- 
malleable  or  not-dense  or  not-metallic."  There  would  be 
seven  distinct  alternatives,  and  this  would  be  absurd. 

I  must  remark,  in  the  first  place,  that  I  wholly  fail  to  see 
the  absurdity.  If  you  mean  to  exhaust  the  cases  which 
exclude  the  term  "  malleable-dense-metal,"  the  absurdity  would 
lie  in  their  number  being  less  than  what  follows  from  the 
number  of  possible  combinations.  But  if  you  mean  to  say 
that,  if  "  or  "  is  exclusive,  you  can  not  deny  the  term  which  is 
offered  unless  you  set  out  all  the  cases  which  exclude  it,  then 
this  is  just  the  mistake  we  have  been  considering.  In  "not- 
malleable  or  not-dense  or  not-metallic"  the  disjoined  are 
incompatible,  but  the  full  possibilities  are  not  set  out.  You 
must  understand  with  each  "  or "  the  implication  of  "  failing 
that."  "  Not  malleable  "  does  not  mean  the  isolated  presence 
of  non-malleability.  It  is  not  one  possibility  :  it  is  a  class  that 
covers  several.  It  means  the  absence  of  malleability,  whether 
the  subject  is  metallic  or  not-metallic,  dense  or  not-dense. 
You  may  fairly  object  that  combinations  are  ignored,  or  else 
that  the  term  "  not-malleable  "  is  ambiguous,  since  it  is  used  to 
cover  a  number  of  cases.  But  these  technical  objections  would 
have  little  importance,  and  they  do  nothing  to  show  that  "  or  " 
does  anything  but  rigidly  disjoin. 

§  II.  Despite  my  respect  for  Professor  Jevons,/ 1  can  not 
admit  any  possible  instance  in  which  alternatives  are  not 
exclusive.  I  confess  I  should  despair  of  human  language,  if 
such  distinctions  as  separate  "  and  "  from  "  or  "  could  be  broken 
down.  And,  when  I  examine  the  further  evidence  produced, 
it  either  turns  on  the  inaccurate  modes  of  expression  we  have 
lately  discussed,  or  consists  in  what  I  must  be  allowed  to  call 
a  most  simple  confusion.  We  are  told  that  the  expressions 
"wreath  or  anadem,"  or  again  "unstain'd  by  gold  or  fee" 
(Jevons,  p.  70),  show  that  "or"  may  sometimes  be  non- 
exclusive. But  this  is  quite  erroneous.  The  alternatives  are 
meant  to  be  rigidly  incompatible.  The  distinction  is  however 
not  applied  to  the  thing,  but  simply  to  the  names.      If  we 


128  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

suppose  that  the  terms  are  quite  synonymous,  then  "wreath 
or  anadem "  means  "  you  may  call  it  by  either  name  you 
please."  The  thing  has  two  titles,  one  of  which  is  at  your 
service.  I  hardly  think  Professor  Jevons  would  assert  that  we 
are  asked  to  use  both  names  at  oftce.  So,  if  "  fee  "  is  not  meant 
to  be  distinct  from  "gold,"  the  assertion  is  that  there  is  no 
stain  arising  from  the  thing  you  may  term  indifferently  gold 
or  fee.  The  idea  of  your  wanting  to  say  both  at  once  is  quite 
ignored. 

I  will  try  to  make  the  matter  clearer  by  inventing  a  piece 
of  imaginary  dialogue.  A.  Who  is  the  greatest  Roman  poet  ? 
B.  His  name  is  Virgil.  A.  What,  not  Vergilius }  B.  Yes, 
Virgil  or  Vergilius.  A.  I  understand  :  he  has  two  names. 
I  will  call  him  henceforth  "  Vergilius-Virgil,"  and  then  I  shall 
be  safe.  B.  Excuse  me  :  in  that  case  you  must  be  wrong. 
You  may  call  him  by  either  of  the  names  you  please,  but  not 
by  both  of  them  at  once. 

It  is  not  worth  while  to  multiply  illustrations.  In  every 
instance  that  can  be  produced,  we  have  either  a  loose  mode  of 
common  speech,  or  else  the  "or"  denotes  incompatibility, 
whether  that  lie  in  the  simultaneous  use  of  alternative  names, 
or  in  the  facts  themselves. 

§  12.  The  mere  statement,  of  course,  may  fail  to  tell  us 
which  of  these  incompatibilities  is  before  us.  And  no  one 
can  deny  that  alternatives  are  often  presented  in  a  very 
inaccurate  way.  It  is  an  excellent  thing  in  all  these  questions 
to  refer  to  the  common  usages  of  language,  but  we  must 
remember  that  in  those  usages,  besides  what  one  calls  "  un- 
conscious logic,"  there  also  may  lurk  mere  looseness  and  care- 
lessness. It  may  not  be  amiss  to  illustrate  the  mistake  we 
have  just  been  discussing,  by  a  parallel  ambiguity  in  the 
hypothetical  judgment.  It  is,  of  course,  the  established 
doctrine  that,  while  you  may  argue  from  ground  to  conse- 
quence, you  can  not  demonstrate  from  consequence  to  ground. 
And,  although  from  a  metaphysical  point  of  view  this 
doctrine  is  certainly  open  to  doubt,  still  for  logical  purposes 
it  is  sufficiently  valid.  But  yet,  by  appealing  to  loose  ex- 
pressions, we  might  show  that  the  ground  is  the  only  ground, 
and  can  therefore  be  inferred  from  the  presence  of  the  conse- 


Chap.  IV.]  THE  DISJUNCTIVE  JUDGMENT.  1 29 

quence.  Sigwart  has  called  attention  to  these  cases  {Logik,  I. 
243  ;  and  Beitrdge,  59.).  "  If  you  run  hard  you  will  catch 
him,"  is  often  an  indirect  way  of  saying,  "  You  will  not  catch 
him  tmless  you  run  hard."  But  such  mere  loose  phrases  are 
no  valid  reason  for  impugning  the  doctrine  that,  unless  this 
fact  is  specially  stated,  the  condition  is  not  given  as  a  sine  qua 
non.  When  the  context  shows  that  our  expressions  are  not 
to  be  strictly  interpreted,  we  are  at  liberty  to  take  "  either — 
or  "as  compatible,  and  "if"  may  be  the  same  as  "not  unless." 
But  we  should  remember  that  what  a  thing  can  pass  for  may 
differ  widely  from  what  it  really  is. 

§  13.  It  is  time  we  left  these  misleading  errors  to  return  to 
the  discussion  of  the  matter  itself.  The  detail  of  the  process 
in  disjunctive  judgments  can  not  fully  be  dealt  with  till  we 
come  to  inference.  But  here  we  may  partly  prepare  the 
ground. 

In  the  first  place,  as  we  shall  see  in  the  following  chapter, 
disjunction  does  not  rest  on  Excluded  Middle.  The  latter 
is  merely  a  case  of  disjunction. 

"  A  is  ^  or  ^"  asserts,  as  we  saw,  that'A  exists  and  possesses 
a  quality.  That  quality,  further,  falls  within  be.  It  is  af- 
firmed to  be  what  is  common  to  both,  and  it  is  stated  also  to 
be  further  determinable  within  be.  In  other  words,  it  excludes 
all  disparates  of  both  b  and  c. 

We  have  seen  this  above,  and  the  point  I  wish  here  to 
bring  forward  is  the  following.  How  do  we  know,  and  how 
can  we  know,  that  there  is  not  a  disparate  of  be  and  which  is 
compatible  with  A  ?  All  rests  upon  this  ;  and  what  does  this 
rest  on  ? 

We  must  answer,  for  the  present,  that  it  rests  on  our 
impotence.  There  is  no  great  principle  on  which  we  can 
stand.  We  can  not  find  any  opposite  of  b  or  opposite  of  c 
which  is  not  also  an  opposite  of  A  ;  and  we  boldly  assume 
that,  because  we  find  none,  therefore  there  is  none.  The 
conclusion  from  impotence  may  itself  seem  impotent,  but,  as 
we  shall  hereafter  see,  there  remains  some  doubt  if  it  may  not 
in  the  end  be  taken  as  the  ground  and  the  sole  ground  we  have 
for  believing  anything  (Book  III.  II.  Chapter  III). 

§  14.  We  may  state  the  whole  matter  once  more  thus. 

K 


130  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

"  A  is  <^  or  ^ "  may  be  expressed  by  (i)  If  A  is  <^  it  is 
not  c,  and  If  A  is  ^  it  is  not  b,  (ii)  If  A  is  not  h  then  it  is  c, 
and  If  A  is  not  c  then  it  must  be  b.  The  first  two  hypothe- 
tical statements  are  erected  on  the  knowledge  that  b  and  c 
as  predicates  of  A  are  incompatible,  or  that  Kbc  can  not 
possibly  exist. 

The  second  pair  are  based  on  the  assumption  that,  because 
we  do  not  find  a  predicate  of  A  which  excludes  b  or  ^,  there- 
fore there  is  none.  Every  opposite  of  b  or  of  ^,  that  we  find,  is 
an  opposite  of  A.  Hence  there  remains  this  result ;  within  the 
limit  of  A  there  is  no  wo\.-b  but  ^,  and  no  not-^  but  b :  and  A 
must  have  some  further  quality.  This  is  the  ground  for  our 
second  two  hypotheticals. 

So  we  see  the  essence  of  disjunctive  judgment  is  not  got 
by  calling  it  a  combination  of  supposals.  It  has  a  distinctive 
character  of  its  own.  It  first  takes  a  predicate  known  within 
limits,  and  defined  by  exclusion,  and  then  further  defines  it 
by  hypothetical  exclusion.  It  rests  on  the  assumption  that 
we  have  the  whole  field,  and  by  removing  parts  can  determine 
the  residue.  It  supposes  in  short  a  kind  of  omniscience. 
Its  assertion  again,  if  not  quite  categorical,  is  certainly  not 
quite  hypothetical.  It  involves  both  these  elements.  And  it 
implies,  in  addition,  a  process  of  inference  which  will  give  us 
cause  for  reflection  in  the  future. 


(     131     ) 


CHAPTER  V. 

THE   PRINCIPLES  OF  IDENTITY,  CONTRADICTION,  EXCLUDED 
MIDDLE,   AND   DOUBLE   NEGATION. 

§  I.  After  discussing  negative  and  disjunctive  judgments, 
we  may  deal  at  once  with  the  so-called  "  Principles  "  of  Iden- 
tity, Contradiction,  and  Excluded  Middle ;  and  we  will  add 
some  remarks  on  Double  Negation. 

The  principle  of  Identity  is  often  stated  in  the  form  of  a 
tautology,  "  A  is  A."  If  this  really  means  that  no  difference 
exists  on  the  two  sides  of  the  judgment,  we  may  dismiss 
it  at  once.  It  is  no  judgment  at  all.  As  Hegel  tells  us,  it 
sins  against  the  very  form  of  judgment  ;  for,  while  professing 
to  say  something,  it  really  says  nothing.  It  does  not  even 
assert  identity.  For  identity  without  difference  is  nothing  at 
all.  It  takes  two  to  make  the  same,  and  the  least  we  can  have 
is  some  change  of  event  in  a  self-same  thing,  or  the  return 
to  that  thing  from  some  suggested  difference.  For,  otherwise, 
to  say  "  It  is  the  same  as  itself"  would  be  quite  unmeaning.  We 
could  not  even  have  the  appearance  of  judgment  in  "A  is  A," 
if  we  had  not  at  least  the  difference  of  position  in  the  different 
A's  ;  and  we  can  not  have  the  reality  of  judgment,  unless  some 
difference  actually  enters  into  the  content  of  what  we  assert. 

§  2.  We  never  at  any  time  wish  to  use  tautologies.  No 
one  is  so  foolish  in  ordinary  life  as  to  try  to  assert  without 
some  difference.  We  say  indeed  "  I  am  myself,"  and  "  Man  is 
man  and  master  of  his  fate."  But  such  sayings  as  these  are 
no  tautologies.  They  emphasize  an  attribute  of  the  subject 
which  some  consideration,  or  passing  change,  may  have 
threatened  to  obscure  ;  and  to  understand  them  rightly  we 
must  always  supply  "  for  all  that,"  "  notwithstanding,"  or  again. 


K  2 


132  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

"analytical  judgments  "*  with  tautologous  statements.  In  the 
former  the  predicate  is  part  of  the  content  of  the  conception 
A,  which  stands  in  the  place  of,  and  appears  as,  the  subject. 
But  in  every  judgment  of  every  kind  a  synthesis  is  asserted. 
The  synthesis  in  Kant's  analytical  judgment  holds  good  with- 
in the  sphere  of  the  conception  ;  and  the  real  subject  is  not  the 
whole  of  A,  but  is  certain  other  attributes  of  A  which  are  not  the 
attribute  asserted  in  the  predicate.  In  "All  bodies  are  ex- 
tended "  what  we  mean  to  assert  is  the  connection,  within  the 
subject  "bodies,"  of  extension  with  some  other  property  of 
bodies.  And  even  if  "  extended  "  and  "  body  "  were  synony- 
mous, we  still  might  be  very  far  from  tautology.  As  against 
some  incompatible  suggestion,  we  might  mean  to  assert  that, 
after  all  misapprehension  and  improper  treatment,  the  extended 
is  none  the  less  the  extended.  And,  again,  we  might  be  making 
a  real  assertion  of  a  verbal  nature.  We  might  mean  that, 
despite  their  difference  as  words,  the  meaning  of  "  body  "  and 
''  extended  "  was  the  same.  But  mere  tautology  with  deliberate 
purpose  we  never  commit.  Every  judgment  is  essentially 
synthetical. 

§  3.  The  axiom  of  Identity,  if  we  take  it  in  the  sense  of  a 
principle  of  tautology,  is  no  more  than  the  explicit  statement 
of  an  error.  And  the  question  is,  would  it  not  be  better  to 
banish  irrevocably  from  the  field  of  logic  such  a  source  of 
mistake  }  If  the  axiom  of  Identity  is  not  just  as  much  an 
axiom  of  Difference,  then,  whatever  shape  we  like  to  give  it,  it 
is  not  a  principle  of  analytical  judgments  or  of  any  other 
judgments  at  all.  On  the  other  hand,  perhaps  something  may 
be  gained  if  a  traditional  form  can  get  a  meaning  which  con- 
veys vital  truth.  Let  us  try  to  interpret  the  principle  of 
Identity  in  such  a  way  that  it  may  really  be  an  axiom. 

§  4.  We  might  take  it  to  mean  that  in  every  judgment  we 
assert  the  identity  of  subject  and  predicate.  Every  connec- 
tion of  elements  we  affirm,  in  short  all  relations  and  every 
difference,  holds  good  only  within  a  whole  of  fact.  All  attri- 
butes imply  the  identity  of  a  subject.  And  taken  in  this  sense 
the  principle  of  Identity  would  certainly  be  true.      But  this 

*  This  is  not  the  sense  in  which  I  have  used  "  analytical."  p,  48. 


Chaf.  v.]  the   principle   OF   IDENTITY.  1 33 

perhaps  is  not  the  meaning  which,  for  logical  purposes,  it  is 
best  to  mark  specially. 

§  5.  There  remains  a  most  important  principle  which, 
whether  it  be  true  or  open  to  criticism,  is  at  least  the  sine  qua 
no?i  of  inference.  And  we  can  not  do  better  than  give  this  the 
name  of  principle  of  Identity,  since  its  essence  is  to  emphasize 
sameness  in  despite  of  difference.  What  is  this  principle  ?  It 
runs  thus  :  "  Truth  is  at  all  times  true,"  or,  "  Once  true  always 
true,  once  false  always  false.  Truth  is  not  only  independent 
of  me,  but  it  does  not  depend  upon  change  and  chance.  No 
alteration  in  space  or  time,  no  possible  difference  of  any  event 
or  context,  can  make  truth  falsehood.  If  that  which  I  say  is 
really  true,  then  it  stands  for  ever." 

So  stated  the  principle  is  not  very  clear,  but  perhaps  it 
will  find  acceptance  with  most  readers.  What  it  means,  how- 
ever, is  much  more  definite,  and  will  be  much  less  welcome. 
The  real  axiom  of  Identity  is  this  :  What  is  true  in  one  context 
is  true  in  aiiother.  Or,  If  any  truth  is  stated  so  that  a  change 
in  events  will  make  it  false,  then  it  is  not  a  genuine  truth  at 
all. 

§  6.  To  most  readers  this  axiom,  I  have  little  doubt,  will 
seem  a  false  statement.  For  the  present  it  may  stand  to  serve 
as  a  test  if  our  previous  discussions  (Chap.  11.)  have  been 
understood.  If  every  judgment  in  the  end  is  hypothetical, 
except  those  not  directly  concerned  with  phenomena — if  each 
merely  asserts  a  connection  of  adjectives,  in  this  sense  that 
giveji  A  then  B  must  follow — we  see  at  once  that  under  any 
conditions  they  will  always  be  true.  And  we  shall  see  here- 
after that  in  every  inference  this  result  is  assumed  as  a  principle 
of  reasoning,  and  that  we  can  not  argue  one  step  without  it. 

§  7.  We  saw  that  such  judgments  as  "  I  have  a  toothache," 
in  their  sensuous  form,  are  not  really  true.  They  fail  and 
come  short  of  categorical  truth,  and  they  hardly  have  attained 
to  hypothetical.  To  make  them  true  we  should  have  to  give 
the  conditions  of  the  toothache,  in  such  a  way  that  the  con- 
nection would  hold  beyond  the  present  case.  When  the 
judgment  gave  the  toothache  as  the  consequent  coming  ac- 
cording to  law  from  the  ground,  when  the  judgment  had  thus 
become   universal,    and,   becoming   this,  had   become   hypo- 


134  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

thetical,  then  at  last  it  would  be  really  true,  and  its  truth 
would  be  unconditional  and  eternal. 

I  know  how  absurd  such  a  statement  sounds.  It  is  impos- 
sible, I  admit,  however  much  we  believe  it,  not  to  find  it  in  a 
certain  respect  ridiculous.  That  I  do  not  complain  of,  for  it 
is  not  our  fault.  But  it  is  our  fault  if  the  common  view  does 
not  seem  more  ridiculous.  I  say  that  "  I  have  a  toothache  " 
to-day.  It  is  gone  to-morrow.  Has  my  former  judgment 
become  therefore  false  ?  The  popular  view  would  loudly  protest 
that  it  still  is  true,  for  I  had  a  toothache,  and  the  judgment  now 
holds  good  of  the  past.  But  what  that  comes  to  is  simply 
this.  The  judgment  is  true  because  answering  to  fact.  The 
fact  alters  so  that  it  does  not  answer  ;  and  yet  the  judgment 
is  still  called  true,  because  of  something  that  does  not  exist. 
Can  anything  be  more  inconsistent  and  absurd  t  If  the 
change  of  circumstance  and  change  of  day  is  not  a  fresh  con- 
text which  falsifies  this  truth,  why  should  any  change  of 
context  falsify  any  truth  }  And  if  changed  conditions  make 
any  truth  false,  why  should  not  all  truth  be  in  perpetual  flux, 
and  be  true  or  false  with  the  fashion  of  the  moment } 

§  8.  We  shall  discuss  this  question  more  fully  hereafte  * 
(Bk.  11.  Part  I.),  but  may  here  anticipate  a  misunderstanding. 
To  ask  "  Does  space  or  time  make  no  difference  "  is  wholly  to 
ignore  the  meaning  of  our  principle.  We  ask  in  reply,  Does 
this  difference  enter  into  the  content  of  A  ?  If  it  does,  then 
A  becomes  perceptibly  diverse,  and  we  confessedly  have  left 
the  sphere  of  our  principle.  But,  if  it  does  not  so  enter,  then 
the  truth  of  A  is  considered  in  abstraction  from  spaces  and 
times,  and  their  differences  are  confessedly  irrelevant  to  its 
truth.  We  thus  meet  the  objection  by  offering  a  dilemma. 
You  have  abstracted  from  the  differences  of  space  and  time, 
or  you  have  not  done  so.  In  the  latter  case  your  subject 
itself  is  different ;  in  the  former  case  it  is  you  yourself  who 
have  excluded  the  difference. 

We  may  indeed  on  the  other  side  be  assailed  with  an  ob- 
jection. We  may  be  asked,  "  What  now  has  become  of  the 
identity  }  Has  it  not  disappeared  together  with  the  differ- 
ences ?  For  if  the  different  contexts  are  not  allowed  to  enter 
into  the  subject,  how  then  can  we  say  what  is  true  in  ohe  con- 


Chap.  V.]         THE   PRINCIPLE  OF  CONTRADICTION.  1 35 

text  is  true  in  another  ?  It  will  not  be  true  in  any  context  at 
all."  But  we  answer,  The  identity  is  not  contained  in  the  judg- 
ment "  S-P,"  since  that  takes  no  kind  of  account  of  the  differ- 
ences. The  identity  lies  in  the  judgment,  "  S-P  is  true  every- 
where and  always."  It  is  this  "  everywhere  "  and  "  always  " 
that  supply  the  difference  against  which  S-P  becomes  an 
identity.  The  predicate  attributed  to  the  real  belongs  to  it 
despite  the  difference  of  its  diverse  appearances.  We  do  not 
say  the  appearances  are  always  the  same,  but  the  quality  keeps 
its  nature  throughout  the  appearances.  And  with  this  reply 
we  must  here  content  ourselves. 

§  9.  When  we  come  to  discuss  the  nature  of  inference  we 
shall  see  more  fully  the  bearing  of  the  principle.  It  stands 
here  on  the  result  of  our  former  enquiries,  that  every  judgment, 
if  it  really  is  true,  asserts  some  quality  of  that  ultimate  real 
which  is  not  altered  by  the  flux  of  events.  This  is  not  the 
place  for  metaphysical  discussion,  or  we  might  be  tempted  to 
ask  if  identity  was  not  implied  in  our  view  of  the  real.  For  if 
anything  is  individual  it  is  self-same  throughout,  and  in  all 
diversity  must  maintain  its  character. 

THE  PRINCIPLE  OF  CONTRADICTION. 

§  10.  Like  the  principle  of  Identity,  the.  principle  of 
Contradiction  has  been  often  misunderstood.  And  in  the  end 
it  must  always  touch  on  a  field  of  metaphysical  debate.  But, 
for  logical  purposes,  I  think  it  is  easy  to  formulate  it  in  a 
satisfactory  way. 

It  is  necessary  before  all  things  to  bear  in  mind  that  the 
axiom  does  not  in  any  way  explain,  that  it  can  not  and  must 
not  attempt  to  account  for  the  existence  of  opposites.  That 
disparates  or  incompatibles  or  contraries  exist,  is  the  fact  it  is 
based  on.  It  takes  for  granted  the  nature  of  things  in  which 
certain  elements  are  exclusive  of  others,  and  it  gives  not  the 
smallest  reason  for  the  world  being  such  in  nature  and  not 
quite  otherwise.  If  we  ever  forget  this,  the  Law  of  Contra- 
diction will  become  a  copious  source  of  illusion. 

§  II.  If  the  principle  of  Contradiction  states  a  fact,  it  says 
no  more  than  that  the  disparate  is  disparate,  that  the  exclusive, 


136  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

despite  all  attempts  to  persuade  it,  remains  incompatible. 
Again,  if  we  take  it  as  laying  down  a  rule,  all  it  says  is,  "  Do 
not  try  to  combine  in  thought  what  is  really  contrary.  When 
you  add  any  quality  to  any  subject,  do  not  treat  the  subject 
as  if  it  were  not  altered.  When  you  add  a  quality,  which  not 
only  removes  the  subject  as  it  was,  but  removes  it  altogether, 
then  do  not  treat  it  as  if  it  remained."  This  is  all  the  meaning 
it  is  safe  to  give  to  the  axiom  of  Contradiction  ;  and  this 
meaning,  I  think,  will  at  once  be  clear,  if  we  bear  in  mind  our 
former  discussions.  The  contrary  is  always  the  base  of  the 
contradictory,  and  the  latter  is  the  general  idea  of  the  contrary. 
Not-A  for  example  is  any  and  every  possible  contrary  of  A 
(Chap.  III.  §  16). 

§  12.  We  have  to  avoid,  in  dealing  with  Contradiction,  the 
same  mistake  that  we  found  had  obscured  the  nature  of 
Identity.  We  there  were  told  to  produce  tautologies,  and 
here  we  are  by  certain  persons  forbidden  to  produce  anything 
else.  "  A  is  not  not-A  "  may  be  taken  to  mean  that  A  can 
be  nothing  but  what  is  simply  A.  This  is,  once  again,  the 
erroneous  assertion  of  mere  abstract  identity  without  any 
difference.  It  is  ordering  us  to  deny  as  a  quality  of  A  every- 
thing that  is  different  from  A,  and  in  this  sense  not-A.  But 
differents  and  disparates  should  never  be  confused.  The 
former  do  not  exclude  one  another  ;  they  only  exclude  the 
denial  of  their  difference.  The  disparate  of  A  can  never  be 
found  together  with  A  in  any  possible  subject,  or  be  joined  to  it 
in  the  relation  of  subject  and  attribute.  The  different  from  A 
does  not  exclude,  unless  you  attempt  to  identify  it  with  A.  It 
is  not  A  generally,  but  one  single  relation  to  A,  which  it  repels. 

As  we  saw  before,  there  is  no  logical  principle  which  will 
tell  us  what  qualities  are  really  disparate.  Metaphysics, 
indeed,  must  ask  itself  the  question  if  any  further  account  can 
be  given  of  incompatibility.  It  must  recognize  the  problem, 
if  it  can  not  solve  it.  We  might  remark  that  no  thing  excludes 
any  other  so  long  as  they  are  able  to  remain  side  by  side,  that 
incompatibility  begins  when  you  occupy  the  same  area ;  and 
we  might  be  tempted  to  conclude  that  in  space  would  be 
found  the  key  of  our  puzzle.  But  such  other  experiences  as 
that   assertion    and  denial,  or  pain  and  pleasure,  are  incom- 


Chap.  V.]         THE   PRINCIPLE   OF   CONTRADICTION.  13/ 

patible,  would  soon  force  us  to  see  that  our  explanation  is  in- 
sufficient. But  in  logic  we  are  not  called  upon  to  discuss  the 
principle  but  rest  upon  the  fact.  Certain  elements  we  find  <3:r^  in- 
compatible ;  and,  where  they  are  so,  we  must  treat  them  as  such. 

§  1 3.  There  is  no  real  question  of  principle  involved  in  such 
different  ways  of  stating  the  axiom  as  "  A  is  not  not-A,"  "  A 
is  not  both  b  and  not-<^,"  "  A  can  not  at  once  both  be  and  not 
be."  For  if  A  were  not-A,  it  would  be  so  because  it  had  some 
quality  contrary  to  A.  So  also,  if  A  has  a  quality  b,  it  could 
only  be  wo\.-b  by  virtue  of  a  quality  disparate  with  b.  And 
again,  if  A  both  were  and  were  not,  that  would  be  because 
the  ultimate  reality  had  contrary  qualities.  The  character  in 
which  it  accepted  A,  would  be  opposite  to  the  quality  which 
excluded  A  from  existence.  Under  varieties  of  detail  we  find 
the  same  basis,  repulsion  of  disparates. 

A  simple  method  of  stating  the  principle  is  to  say,  "  Denial 
and  affirmation  of  the  self-same  judgment  is  wholly  in- 
admissible." And  this  does  not  mean  that  if  a  miracle  in 
psychology  were  brought  about,  and  the  mind  did  judge  both 
affirmatively  and  negatively,  both  judgments  might  be  true. 
It  means  that,  if  at  once  you  affirm  and  deny,  you  must  be 
speaking  falsely.  For  denial  asserts  the  positive  contrary  of 
affirmation.  In  the  nature  of  things  (this  is  what  it  all  comes 
to)  there  are  certain  elements  which  either  can  not  be  conjoined 
at  all,  or  can  not  be  conjoined  in  some  special  way  ;  and  the 
nature  of  things  must  be  respected  by  logic. 

§  14.  If  we  wish  to  show  that  our  axiom  is  only  the  other 
side  of  the  Law  of  Identity,  we  may  state  it  thus,  "  Truth  is 
unchangeable,  and,  as  disparate  assertions  alter  one  another, 
they  can  not  be  true."  And  again,  if  we  desire  to  glance  in 
passing  at  the  metaphysical  side  of  the  matter,  we  may 
remind  ourselves  that  the  real  is  individual,  and  the  individual 
is  harmonious  and  self-consistent.  It  does  not  fly  apart,  as 
it  would  if  its  qualities  were  internally  discrepant. 

§  15.  Having  now  said  all  that  I  desire  to  say,  I  would 
gladly  pass  on.  For,  notwithstanding  the  metaphysics  into 
which  we  have  dipped,  I  am  anxious  to  keep  logic,  so  far  as  is 
possible,  clear  of  first  principles.     But  in  the  present  instance 


138  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

the  law  of  Contradiction  has  had  the  misfortune  to  be  flatly- 
denied  from  a  certain  theory  of  the  nature  of  things.  So  far 
is  that  law  (it  has  been  contended)  from  being  the  truth,  that 
in  the  nature  of  things  contradiction  exists.  It  is  the  fact  that 
opposites  are  conjoined,  and  they  are  to  be  found  as  disparate 
moments  of  a  single  identity. 

I  need  hardly  say  that  it  is  not  my  intention  compen- 
diously to  dispose  in  a  single  paragraph  of  a  system  which, 
with  all  its  shortcomings,  has  been  worked  over  as  wide  an 
area  of  experience  as  any  system  offered  in  its  place.  My  one 
idea  here  is  to  disarm  opposition  to  the  axiom  of  contra- 
diction, as  it  stands  above.  But  I  clearly  recognize  that,  if 
not-A  were  taken  as  a  pure  negation,  no  compromise  would  be 
possible.  You  would  then  have  to  choose  between  the  axiom  of 
contradiction  and  the  dialectical  method. 

I  will  say,  in  the  first  place,  that  whatever  is  conjoined  is 
therefore  ipso  facto  shown  not  to  be  disparate.  If  the 
elements  co-exist,  cadit  qucestio :  there  is  no  contradiction,  for 
there  can  be  no  contraries.  And,  saying  so  much,  I  feel 
tempted  to  retire.  But  yet  with  so  much  I  shall  hardly 
escape.  "  Have  not  we  got,"  I  hear  the  words  called  after  me, 
"  have  we  not  got  elements  which  any  one  can  see  negate  one 
another,  so  that,  while  one  is,  the  other  can  not  be  ;  and  yet 
have  we  not  got  very  many  conceptions  in  which  these 
discrepants  somehow  co-exist .?  It  is  all  very  well  to  say, 
'  then  not  contrary  ; '  but  try  them,  and  see  if  they  are  not 
exclusive." 

It  is  plain  that  I  must  stand  and  say  something  in  reply. 
But  I  think  I  shall  hardly  be  so  foolish  as  to  answer,  "  These 
conceptions  of  yours  are  merely  phenomenal.  Come  to  us  and 
learn  that  knowledge  is  relative,  and  with  us  give  up  the 
Thing-in-itself."  For  without  knowing  all  that  would  be  poured 
on  my  head,  I  can  guess  some  part  of  what  I  should  provoke. 
*'  You  say  '  give  up  the  Thing-in-itself  }  Why  that  is  all  that 
you  have  not  given  up.  You  profess  that  your  knowledge  is 
only  phenomenal,  and  then  you  make  the  law  of  Contradiction 
valid  of  the  Absolute,  so  that  what  it  excludes  you  are 
able  to  know  is  not  the  Absolute.  That  is  surely  inconsistent. 
And   then,  for  the   sake   of  saving   from   contradiction   this 


Chap.  V.]         THE   PRINCIPLE   OF   CONTRADICTION.  1 39 

wretched  ghost  of  a  Thing-in-itself,  you  are  ready  to  plunge 
the  whole  world  of  phenomena,  everything  you  know  or 
can  know,  into  utter  confusion.  You  are  willing  to  turn 
every  fact  into  nonsense,  so  long  as  this  Thing-in-itself  is 
saved.  It  is  plain,  then,  for  which  you  really  care  most.  And 
as  for  ^relativity,'  it  is  you  yourselves  who  violate  that 
principle.  Your  turning  of  the  relative  into  hard  and  fast 
contraries  is  just  what  has  brought  you  to  your  miserable 
pass."  I  confess  I  should  hardly  care  to  subject  myself  to  all 
these  insults  ;  and  I  had  rather  Mr.  Spencer,  or  some  other 
great  authority — whoever  may  feel  himself  able  to  bear  them, 
or  unable  to  understand  them — should  take  them  on  himself. 

If  I  chose  to  turn  and  provoke  a  contest,  I  know  of 
another  weapon  I  might  use.  I  might  say,  "  Your  concep- 
tions are  partial  illusions.  They  are  crude  popular  modes  of 
representing  a  reality  whose  nature  can  not  be  so  pourtrayed. 
And  the  business  of  philosophy  is  to  purify  these  ideas,  and 
never  to  leave  them  until,  by  removal  of  their  contradictions, 
they  are  made  quite  adequate  to  the  actual  fact."  But,  after 
all,  perhaps  I  could  only  say  this  for  the  sake  of  controversy, 
and  controversy  is  what  I  am  anxious  to  avoid.  And  for  this 
end  I  think  that  some  compromise  may  perhaps  be  come  to. 
Without  calling  in  question  the  reality  of  negation,  and  the 
identity  of  opposites,  are  we  sure  that  we  can  not  under- 
stand that  doctrine  in  a  sense  which  will  bear  with  the  axiom 
of  Contradiction  }  This  axiom  is  not  like  the  principle  of 
Identity.  It  is  a  very  old  and  most  harmless  veteran  ;  and  for 
myself  I  should  never  have  the  heart  to  attack  it,  unless  with  a 
view  to  astonish  common-sense  and  petrify  my  enemies.  And 
in  metaphysics  we  can  always  do  that  in  many  other  ways. 

What  I  mean  is  this.  Supposing  that,  in  such  a  case  as 
continuity,  we  seem  to  find  contradictions  united,  and  A  to  be 
d  and  not-^  at  once,  this  may  yet  be  reconciled  with  the  axiom 
of  Contradiction.  A  we  say  is  composed  of  d  and  not-<^  ;  for, 
dissecting  A,  we  arrive  at  these  elements,  and,  uniting  these, 
we  get  A  once  more.  But  the  question  is,  while  these 
elements  are  in  A,  can  they  be  said,  while  there,  to  exist  in 
their  fully  disparate  character  of  ^  and  not-^  f  I  do  not  mean 
to  suggest  that  the  union  of  contraries  may  be  that  misunder- 


140  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

Standing  of  the  fact  which  is  our  only  way  to  understand  it. 
For,  if  I  felt  sure  myself  that  this  were  true,  I  know  it  is  a 
heresy  too  painful  to  be  borne.  But,  in  the  object  and  within 
the  whole,  the  truth  may  be  that  we  never  really  do  have 
these  disparates.  We  only  have  moments  which  would  be 
incompatible  if  they  really  were  separate,  but,  conjoined 
together,  have  been  subdued  into  something  within  the 
character  of  the  whole.  If  we  so  can  understand  the  identity 
of  opposites — and  I  am  not  sure  that  we  may  not  do  so — then 
the  law  of  Contradiction  flourishes  untouched.  If,  in  coming 
into  one,  the  contraries  as  such  no  longer  exist,  then  where  is 
the  contradiction  t 

But,  I  fear,  I  shall  be  told  that  the  struggle  of  negatives  is 
the  soul  of  the  world,  and  that  it  is  precisely  because  of  their 
identity  that  we  have  their  contradiction.  It  is  true  that  the 
opposition  which  for  ever  breaks  out  leads  to  higher  unity  in 
which  it  is  resolved ;  but  still  the  process  of  negation  is  there. 
It  is  one  side  of  the  world  which  can  not  be  got  rid  of,  and  it  is 
irreconcileable  with  the  non-existence  of  disparates  in  a  single 
subject.  Each  element  of  the  whole,  without  the  other,  is 
incompatible  with  itself ;  but  it  is  none  the  less  incompatible 
with  the  other,  which  for  ever  it  produces  or  rather  becomes. 

I  am  after  all  not  quite  convinced.  If  the  law  of  Contra- 
diction is  objected  against  because,  in  isolating  and  fixing  the 
disparate,  it  becomes  one-sided,  is  it  not  quite  possible  that, 
in  denying  the  law,  we  have  become  one-sided  in  another 
way  t  If  the  negation  itself,  while  negative  on  one  side,  is  on 
the  other  side  the  return  from  itself  to  a  higher  harmony — if, 
that  is  to  say,  the  elements  are  not  disparate  without  each  at 
once,  by  virtue  of  its  disparateness  and  so  far  as  it  is  disparate, 
thereby  ipso  facto  ceasing  to  be  disparate,  then  surely,  in  denying 
the  law  of  Contradiction,  we  ourselves  have  fixed  one  side  of  the 
process,  and  have  treated  the  contrary  as  simply  contrary.  The 
contrary  which  the  law  has  got  in  its  head,  is  the  contrary 
that  entirely  kills  its  opposite,  and  remains  triumphant  on  the 
field  of  battle.  It  is  not  the  contrary  whose  blows  are  suicidal, 
and  whose  defeat  must  always  be  the  doom  of  its  adversary. 
It  is  incompatibles  fixed  as  such,  it  is  disparates  which  wholly 
exclude  one  another  and  have  no  other  side,  that  the  axiom 


Chap.  V.]         THE   PRINCIPLE   OF   CONTRADICTION.  I4I 

speaks  of.  But  dialectical  contraries  are  only  partially  con- 
trary and  it  is  otir  mistake  if  we  keep  back  the  other  side. 
And  if  an  opponent  of  the  law  reminds  me  that  the  existence 
of  these  two  sides  within  one  element  is  just  the  contradic- 
tion, that  in  the  b  which  is  contrary  to  not-^  the  implication 
of  not-^  makes  it  self-contradictory,  then  I  must  be  allowed  to 
say  in  reply  that  I  think  my  objector  has  not  learnt  his  lesson. 
The  not-^  in  b  is  itself  self-disparate,  and  is  just  as  much  b: 
and  so  on  for  ever.  We  never  have  a  mere  one-sided 
contrary. 

But  it  is  one-sided  and  stationary  contraries  that  the 
axiom  contemplates.  It  says  that  they  are  found,  and  no 
sober  man  could  contend  that  they  are  not  found.  No  one 
ever  did  maintain  that  the  dialectical  implication  of  opposites 
could  be  set  going  in  the  case  of  every  conjunction  that  we 
deny.  It  can  hardly  be  maintained  that  there  are  no  disparates, 
except  these  contraries  which  at  the  same  time  imply  each 
other.  And  the  law  of  Contradiction  does  not  say  any  more 
than  that,  when  such  sheer  incompatibles  are  found,  we  must 
not  conjoin  them. 

Its  claims,  if  we  consider  them,  are  so  absurdly  feeble,  it  is 
itself  so  weak  and  perfectly  inoffensive,  that  it  can  not  quarrel, 
for  it  has  not  a  tooth  with  which  to  bite  any  one.  The 
controversy,  first  as  to  our  actual  ability  to  think  in  the  way 
recommended  by  Hegel,  and  secondly  as  to  the  extent  to  which 
his  dialectic  is  found  in  fact,  can  not  only  not  be  settled  by  an 
appeal  to  the  axiom,  but  falls  entirely  outside  its  sphere. 
Starting  from  the  fact  of  the  absolute  refusal  of  certain  elements 
to  come  together,  and  wholly  dependent  upon  that  fact,  so 
soon  as  these  elements  do  come  together  the  axiom  ceases 
forthwith  to  be  applicable.  It  is  based  upon  the  self-consistency 
of  the  real,  but  it  has  no  right  to  represent  that  consistency 
except  as  against  one  kind  of  discrepancy.  So  that,  if  we 
conclude  that  the  dialectic  of  the  real  would  in  the  end  destroy 
its  unity,  that  has  nothing  to  do  with  the  axiom  of  Contradic- 
tion. Like  every  other  question  of  the  kind,  the  validity  of 
dialectic  is  a  question  of  fact,  to  be  discussed  and  settled  upon 
its  own  merits,  and  not  by  an  appeal  to  so-called  "  principles.'* 
And  I  think  I  may  venture   to  hazard  the  remark,  that  one 


142  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

must  not  not  first  take  up  from  uncritical  views  certain 
elements  in  the  form  of  incompatible  disparates,  and  then, 
because  we  find  they  are  conjoined,  fling  out  against  the  laws  of 
Contradiction  and  Excluded  Middle.  They,  such  as  they  are, 
can  be  no  one's  enemy  ;  and  since  no  one  in  the  end  can  per- 
haps disbelieve  in  them,  it  is  better  on  all  accounts  to  let  them 
alone. 

PRINCIPLE  OF  EXCLUDED  MIDDLE. 

§  1 6.  The  axiom  that  every  possible  judgment  must  be 
true  or  false,  we  shall  see  is  based  on  what  may  be  called  a 
principle.  It  is  however  doubtful  if  the  axiom  itself  should 
receive  that  title,  since  it  comes  under  the  head  of  disjunctive 
judgment.  We  must  not  imagine  that  our  axiom  supplies  the 
principle  of  disjunction.  It  is  nerely  one  instance  and  applica- 
tion of  that  principle. 

§  17.  If  we  recall  the  character  of  the  disjunctive  judgment, 
we  shall  remember  that  there  we  had  a  real,  known  to  be 
further  determined.  Its  quality  fell  (i)  within  a  certain  area  ; 
and  (ii)  since  that  area  was  a  region  of  disparates,  the  real 
was  determined  as  one  single  member.  On  this  basis  we  erected 
our  hypothetical,  and  so  the  "  either— or  "  was  completed. 

Excluded  Middle  shows  all  these  characteristics.  In  it  we 
affirm  (i)  that  any  subject  A,  when  the  relation  to  any  quality 
is  suggested,  is  determined  at  once  with  respect  to  that 
predicate  within  the  area  of  position  and  negation,  and  by 
no  relation  which  is  incompatible  with  both.  And  (ii)  we 
assert  that,  within  this  area,  the  subject  is  qualified  as  one 
single  member,  And  then  we  proceed  to  our  "  either — or." 

§  18.  Excluded  Middle  is  one  case  of  disjunction:  it  can 
not  be  considered  co-extensive  with  it.  Its  dual  and  con- 
tradictory alternative  rests  on  the  existence  of  contrary 
opposites.  The  existence  of  exclusives  without  reference  to 
their  number  is  the  ground  of  disjunction,  and  the  special  case 
of  assertion  and  denial  is  developed  from  that  basis  in  the 
way  in  which  contradiction  is  developed  from  exclusion. 
Common  disparate  disjunction  is  the  base,  and  the  dual 
alternative  of  b  and  not-^  rests  entirely  upon  this. 

§  19.  Excluded  Middle  is  one  kind  of  disjunction  :  and  we 


Chap.  V.]  PRINCIPLE   OF   EXCLUDED   MIDDLE.  I43 

must  proceed  to  investigate  the  nature  of  that  kind,  (i) 
Disjunction  asserts  a  common  quality.  In  ''  b  or  not-<^"  the 
common  quality  asserted  of  A  is  that  of  general  relation  to  b,^ 
(ii)  Disjunction  asserts  an  area  of  incompatibles.  Affirmation 
or  denial  of  b  is  here  the  area  within  which  A  falls.  The 
evidence  that  it  does  not  fall  outside  and  that  all  the  dis- 
parates are  completely  given,  may  be  called  my  impotence 
to  fin(^  any  other,  (iii)  Disjunction  attributes  to  the  subject  A 
one  single  element  of  the  area.  And  this  part  of  the  process 
does  not  call  here  for  any  special  remark. 

§  20.  We  find  however,  when  we  investigate  further,  a  point 
in  which  the  axiom  of  Excluded  Middle  goes  beyond  the 
limits  of  disjunctive  judgment.  It  contains  a  further  principle, 
since  it  asserts  a  common  quality  of  all  possible  existence.  It 
says.  Every  real  has  got  a  character  which  determines  it  in 
judgment  with  reference  to  every  possible  predicate.  That 
character  furnishes  the  ground  of  some  judgment  in  respect  of 
every  suggested  relation  to  every  object.  Or,  to  put  the  same 
more  generally  still.  Every  element  of  the  Cosmos  possesses  a 
quality,  which  can  determine  it  logically  in  relation  to  every 
other  element. 

§  21.  This  principle  is  prior  to  the  actual  disjunction.  It 
says  beforehand  that  there  is  a  ground  of  relation,  though  it 
does  not  know  what  the  relation  is.  The  disjunction  proceeds 
from  the  further  result  that  the  relation  falls  within  a 
disparate  sphere.  We  thus  see  that,  on  the  one  hand. 
Excluded  Middle  transcends  disjunction,  since  it  possesses  a 
self-determining  principle  which  disjunction  has  not  got.  On 
the  other  hand,  in  its  further  developement,  it  is  nothing 
whatever  but  a  case  of  disjunction,  and  must  wait  for  the 
sphere  of  disparate  predicates  to  be  given  it  as  a  fact. 

§  22.  The  disjunction  is  completed  by  the  fact  that,  when 
any  predicate  is  suggested,  the  quality  of  every  element  is  a 
ground  of  either  the  affirmation  or  the  denial  of  the  predicate. 
It  compels  us  to  one  and  to  one  alone  ;  for  no  other  alternative 
can  possibly  be  found. 

And  here  the  opposition,  directed  before  against  the  axiom 
of  Contradiction,  must  again  be  confronted.  It  is  false,  we 
are  told,  that  A  must  either  be  c  or  not-^.     We  have  often  to 


144  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

say  "  both,"  and  sometimes  "  neither."  But  I  think  perhaps  the 
discussion  at  the  end  of  the  foregoing  chapter  will  have 
strengthened  us  to  persist.  I  fully  admit  that  often,  when 
challenged  to  reply  Yes  or  No,  it  is  necessary  to  answer  "  Yes 
and  No  "  or  "  Neither."  But,  I  venture  to  think,  that  is  always 
because  the  question  is  ambiguous,  and  is  asked  from  the 
standpoint  of  a  false  alternative.  "  Is  motion  continuous  }  Yes  or 
no. "  I  decline  to  answer  until  you  tell  me  if,  by  saying  Yes, 
I  am  taken  to  deny  that  it  is  also  discrete.  In  that  case 
perhaps,  instead  of  saying  Yes,  I  should  go  so  far  as  to  answer 
No.  There  may  be  a  middle  between  continuity  and  discretion^ 
there  can  be  none  between  continuous  and  not-continuous. 

The  ground  of  the  objection  to  the  Excluded^  Middle  is, 
I  am  bold  enough  to  think,  fallacious.  Given  not  fixed 
disparates  but  dialectical  opposites,  the  existence  of  these 
together  in  one  single  subject  does  not  give  us  the  right  to  a 
negative  judgment.  One  can  not  be  made  use  of  as  the 
positive  ground  on  which  to  build  the  denial  of  the  other. 
One  does  not  wholly  remove  the  other,  and,  failing  to  do  so, 
it  is  not  qualified  as  a  logical  contrary.  For  it  is  only  the 
disparate  which  destroys  its  opposite  that  can  serve  as  the 
base  of  a  negative  judgment.  And,  failing  the  denial  of  one 
quality  through  the  other,  the  answer  must  be  that  both  are 
present,  and  the  denial  of  either  is  wholly  excluded.  But  I 
fear  it  is  hard  altogether  on  this  point  to  effect  a  compromise. 
If  the  negative  of  b  is  ever  simply  not-<^,  and  if  this  is  the 
other  which  is  implicated  with  b  in  one  subject  A,  then  I 
grant  the  Excluded  Middle  disappears.  But,  I  think,  in  this 
case  it  will  carry  along  with  it  enough  to  ruin  what  is  left 
behind.     And  I  must  leave  the  matter  so. 

§  23.  The  Excluded  Middle,  as  we  saw  before,  is  a 
peculiar  case  of  the  disjunctive  judgment ;  and  I  think  this 
insight  may  serve  us  further  to  dispel  some  illusions  which 
have  gathered  round  it. 

In  the  first  place  we  must  not  think  it  is  a  formula,  by 
applying  which  we  can  magically  conjure  elements  of  know- 
ledge from  the  unknown  deep.  It  is  nonsense  to  say  that  it 
gives  us  a  revelation  that  any  subject  must  have  one  of  two 
predicates.     For,  even  if  we  do  not  make  a  logical  mistake 


rCJlTIVERSI 

Chap.   V.]  PRINCIPLE   OF    EXCLUDED   MIDDLE.    ^^  HSl'^-^  ^"^ 

and  really  have  got  contradictory  qualities,  that  is  stiliiT6F==^^^ 

the  right  way  to  put  the  matter.     Denial  is  not  the  predica-  I 
tion  of  a  contradictory ;  and  all  that  Excluded  Middle  tells 

us   is   that,   given   any  possible  element   of  knowledge,  you  \ 

must  be  right  in  either  affirming  or  denying  any  suggestion  \ 
that  is  made  about  that. 

We  learnt,  in  our  chapter  on  the  Disjunctive  Judgment,  \ 

that  this  judgment  must  assume  the  existence  of  its  subject,  \ 

though   that   subject   may  not  be   the  grammatical  subject  \ 

And  when,  in  the  case  of  Excluded  Middle,  we  are  told  it  will  1 

guarantee  us  the  truth  of  either  b  or  not-  /^  as  a  predicate  of  A ,  1 
we  naturally  ask,  "  But  what  guarantees  to  us  the  existence  of 

A  ?  "     And  we  get  no  answer.     Things  in  themselves  either  \ 

are  b  or  are  not  b.     Undoubtedly  so,  but  zvhat  is  the  real  sit^bject  \ 

of  this  statement  f      It  perhaps  after  all  is  not  "  Things-in-  \ 
themselves,"  but  is  ultimate  reality,  which  may  totally  reject 

the  whole  ofifered  synthesis.     In  this  case  we  shall  at  once  be  \ 
able  to  say  that  Things-in-themselves  are  not  anything  at  all 
in   the   real  world,  though,   considered  as  illusions,  they  no           .  j 

doubt   have   qualities.      On    the    other   hand,    if    Things-in-  \ 

themselves  are  taken  as  such  to  have  existence,  then  that  is  \ 

not  proved  by  our  Excluded  Middle,  but  is  a  sheer  assump-  i 
tion  on  which  we  base  it  and  which  it  presupposes. 

§  24.  But  when  we  are  told,  "  Between  the  true  and  the 

false  there  is  a  third  possibility,  the  Unmeaning  "  (Mill,  Logic,  I 

II.  vii.  §  4),  we  must  answer,  "Yes,  an  unmeaning  possibility,  | 

and  therefore  none  at  all."      The  doctrine  that  propositions  \ 

need  neither  be  true  nor  yet  be  false  because  they  may  be  \ 

senseless,  would  introduce,  I   agree,  "  a  large  qualification  "  ] 

into  the  doctrine  of  the  Excluded  Middle.     But  I  am  inclined  I 

to  think  that  this   "  qualification  "   might  be   larger   than    it  ] 

seems   to   be,  and  might  be   operative    perhaps    beyond  the  • 

limits  so  sparingly  assigned  to  it.      But  surely,  on  the  one  1 

hand,  it   is  clear  that  a  proposition  which  has  no  meaning  ^ 

is  no  proposition  ;  and  surely  again,  on  the  other  hand,  it  is  '\ 

clear  that,  if  it  does  mean  anything,  it  is  either  true  or  else  1 

false.     And  when  a  predicate  is  really  known  not  to  be  "  one  ^ 

which  can  in  any  intelligible  sense  be  attributed  to  the  sub-  J 

ject"— is   not   that   itself  ground   enough    for  denial  ?  '   But  \ 

L  \ 


14^  THE  PRINCIPLES  OF  LOGIC.  [Book    I. 

logicians  who  actually  (Mill,  loc.  cit)  are  ready  to  take  divisible 
finitely  and  divisible  infinitely  as  contradictories,  are  justified  in 
expecting  extraordinary  events.  Suppose  these  terms  to  be 
absolutely  disparate,  that  would  hardly  bring  them  under 
Excluded  Middle,  unless  we  are  prepared  to  formulate  the 
axiom  thus :  Whenever  predicates  are  incompatible,  then, 
although  there  be  three  or  more  possibilities,  it  is  certain  that 
one  of  these  two  possibilities  must  always  be  true.  But 
perhaps  this  "  qualification "  might  tend  to  create  more 
difficulties  than  it  solves. 

§  25.  If  we  turn  from  these  somewhat  elementary 
mistakes,  and  consider  the  amount  of  actual  knowledge 
vouchsafed  to  us  by  the  Excluded  Middle,  I  hardly  think  we 
shall  be  much  puffed  up.  We  must  remember  that,  even  if 
we  are  able  to  assert  about  such  a  subject  as  Things-in- 
themselves,  we  must  always  be  on  our  guard  against  an  error. 
We  may  be  affirming  about  the  meaning  of  a  word,  or  about  a 
mere  idea  in  our  heads,  and  may  confuse  these  facts  with 
another  kind  of  fact  (p.  41).  But,  even  supposing  we  keep  quite 
clear  of  this  mistake,  yet  when  we  come  to  negative  judgments 
there  is  ambiguity,  unavoidable  and  ceaseless,  about  the 
positive  ground  of  the  denial.  We  may  penetrate  so  far  into 
hidden  mysteries  as  perhaps  to  be  privileged  solemnly  to 
avouch  that  Things-in-themselves  are  not  three-cornered,  nor 
coloured  rose-red,  nor  pock-marked  nor  dyspeptic.  But  what 
does  this  tell  us .?  What  more  should  we  know,  if  we  spent 
our  breath  and  wasted  our  days  in  endless  denials  of  senseless 
i^uggestions ?  If  the  ground  of  negation  remains  the  same, 
li^ach  particular  denial  asserts  nothing  in  particular  (Chap.  III. 
'pp.  116,  120). 

§  26.  Confined  to  its  limits  the  Excluded  Middle  is  rigidly 
true.  But  you  may  easily  assert  it  in  a  shape  which  would 
exhibit  a  parallel  falsehood  to  those  we  considered  in 
examining  the  Principles  of  Identity  and  Contradiction. 
"Everything,"  we  might  say,  "is  either  simply  the  same  as 
any  other,  or  else  has  nothing  whatever  to  do  with  it." 

Once  again,  in  conclusion,  I  must  call  attention  to  the 
positive  principle  which  underlies  the  Excluded  Middle.  We 
assume  that  every  element  of  knowledge  can  stand  in  some 


Chap.   V.]  PRINCIPLE   OF   EXCLUDED   MIDDLE.  147 

relation  with  every  other  element.  And  we  may  give  this,  if 
we  please,  a  metaphysical  turn,  though  in  doing  so  we  go 
beyond  the  equivalent  of  the  Excluded  Middle.  We  may 
say,  If  the  real  is  harmonious  and  individual,  it  must  exist  in 
its  members  and  must  inter-relate  them. 

§  27.  I  may  notice  by  way  of  appendix  to  this  subject  a 
somewhat  subtle  argument  of  Professor  Jevons,  which  I  regret 
to  state  I  am  unable  to  understand.  He  argues*  that  to  say 
"  A  =  B  or  b''  must  be  incorrect.  For  the  negative  of  "  B  or 
b  "  will  be  B<^,  and  by  consequence  a,  the  negative  of  A,  must 
itself  be  B^.  And  the  objection  to  this  is  that  B<^  =  o.  But 
because  "every  term  has  its  negative  in  thought,"  therefore  the 
negative  of  A  can  not  be  =  o,  and  the  premise  "  A  =  B  or  <^  \ 
is  thus  indirectly  proved  false.  Professor  Jevons  proceeds  to 
draw  from  this  a  general  conclusion  that  any  judgment,  in  the 
form  "A  =  B  or  4"  is  necessarily  erroneous,  and  that  we 
must  write  instead  of  it  "  A  =  AB  or  KbT 

Though  I  fully  agree  with  this  last  result,  yet  Professor 
Jevons'  reasoning,  as  I  understand  it,  appears  to  me  unsound, 
and  I  can  not  reconcile  his  conclusion  with  his  process.  I  will 
take  the  latter  point  first.  It  appears  to  be  right  to  judge 
"  A  =  AB  or  Kbr  But  what  is  the  negative  }  I  suppose  the 
negative  is  A<^B,  and  we  must  conclude  that  a  =  AbB.  But 
the  term  A^B  most  clearly  = .  o.  So  that,  after  all,  we  are 
left  with  a  conclusion  which  proves  the  falsity  of  our  premise. 

The  result  is  thus  out  of  harmony  with  the  argument,  but 
for  all  that  the  result  is  perfectly  true.  It  ts  true  that  we  can 
not  say  "  A  =  B  or  b"  and  I  will  proceed  to  show  w/iy  this 
must  be  true.  We  must  take  it  that  A  has  a  determinate 
quality  ;  but  what  is  merely  B  ox  b  is  anything  whatever.  B^ 
being  nothing,  what  is  simply  not-B(^  will  therefore  be  any- 
thing. And,  as  A  is  something  definite,  "A  =  anything" 
will  of  course  be  false.  The  sphere  "  B  or  ^  "  is  wholly  un- 
limited. 

This  confirms  the  doctrine  we  have  above  adopted  (p.  118). 
If  you  take  not-B  as  the  bare  and  simple  negation  of  B,  it  is 
nothing  at  all.     And  if  you  keep  to  this  sense,  then  "  A  = 

*  Principles^  p.  74.  For  the  meaning  of  Professor  Jevons'  symbols 
I  must  refer  to  his  work. 

L   2 


148  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

not-B  "  could  not  be  true.  The  true  meaning  of  not-B  is  any- 
indefinite  general  quality  which  does  exclude  B.  And,  so 
long  as  A  is  something  definite,  A  can  not  be  this,  I  am 
inclined  to  think  from  the  presence  of  x  {Principles,  pp.  94, 
95)  that  Professor  Jevons  would  agree  with  this  doctrine. 

But  the  conclusion,  which  Professor  Jevons  uses  as  false,  is  not 
only  quite  true,  but  is  the  necessary  result  of  the  true  doctrine 
he  accepts.  Taking  A  as  the  genuine  subject  that  lies  at  th^ 
base  of  the  disjunction,  then  "  ^  —  nothing "  must  follow  at 
once,  since  "  A  is  B  or  not-B  "  does  assume  and  postulate  that 
A  is  real.  If  a  were  anything  but  non-existent,  you  could  not 
use  A  as  the  base  of  a  disjunction.  What  is  wrong  is  not  this 
conclusion  or  its  premises,  but  the  mistaken  idea  about  the 
negative  which  Professor  Jevons  has  embraced. 

I  confess  I  am  not  sure  if  I  apprehend  him  rightly,  but  he 
seems  to  argue  that  the  non-existent  is  not  thinkable,  and 
hence,  because  the  negative  of  everything^  is  thinkable,  you 
must  never  have  a  negative  which  is  non-existent.  Now  I 
admit  that,  if  "  existence  "  is  used  in  the  widest  possible  sense, 
this  argument  is  tenable.  The  unreal,  the  impossible,  and 
the  non-existent  will  every  one  of  them  exist,  provided  they 
are  thinkable.  And,  since  even  nothing  itself  in  this  sense 
exists,  it  is  obvious  the  whole  argument  thus  disappears. 

But,  if  it  does  not  disappear,  and  if  existence  be  taken 
in  anything  like  the  sense  of  reality,  the  argument  becomes 
vicious.  We  have  no  right  to  assume  that  the  contradictory 
of  an  idea  which  is  true,  must  itself  be  real.  Take  for 
instance  the  idea  of  "  reality  "  itself  I  could  not  even  admit  that 
in  thought  all  ideas  are  qualified  by  their  negations,  t  should 
doubt  if  the  highest  term  we  arrive  at  can  be  said  to  have  an 
opposite  even  in  thought,  although  by  an  error  we  are  given 
to  think  so.  But  to  hold  that  what  contradicts  the  real  must 
be  real,  is  a  logical  mistake  which  I  cannot  venture  to  attri- 
bute to  Prof  Jevons. 

I  may  end  with  the  remark  that  it  would  be  entertaining 
and  an  irony  of  fate,  if  the  school  of  "  experience  "  fell  into  the 
cardinal  mistake  of  Hegel.  Prof  Bain's  "  Law  of  Relativity,'* 
approved  by  J.  S.  Mill,  has  at  least  shown  a  tendency  to  drift 
in  that  direction.     "  Our  cognition,  as  it  stands,  is  explained 


Chap.   V.]  DOUBLE   NEGATION.  149 

as  a  mutual  negation  of  the  two  properties.  Each  has  a  posi- 
tive existence  because  of  the  presence  of  the  other  as  its  nega- 
tive" {Emotions,  p.  571).  I  do  not  suggest  that  Prof.  Bain  in 
this  ominous  utterance  really  means  what  he  says,  but  he  means 
quite  enough  to  be  on  the  edge  of  a  precipice.  If  the  school 
of  "  Experience  "  had  any  knowledge  of  the  facts,  they  would 
know  that  the  sin  of  Hegel  consists,  not  at  all  in  the  defect, 
but  in  the  excess  of  "  Relativity."  Once  say  with  Prof  Bain 
that  "  we  know  only  relations  ;  "  once  meaii  (what  he  says)  that 
those  relations  hold  between  positives  and  negatives,  and  you 
have  accepted  the  main  principle  of  orthodox  Hegelianism. 

DOUBLE  NEGATION. 

§  28.  It  is  obvious  that  duplex  negatio  affirmat.  To  say 
"  It  is  false  that  A  is  7iot  B  "  is  equivalent  to  the  positive  asser- 
tion, "  A  is  B."  But  this  is  not  because  the  added  negation 
barely  negates  the  original  judgment.  For  if  that  were  all, 
we  should  be  left  with  nothing.  If  mere  not-A  is  simply  zero, 
then  not-not-A  is,  if  possible,  less.  And  we  must  not  say  that 
negation  presupposes  a  positive  judgment,  which  is  left  in  pos- 
session when  the  negative  is  negated.  For  we  saw  before 
(Chap.  III.  §4)  that  this  positive  judgment  is  not  presupposed. 

§  29.  The  real  reason  why  denial  of  denial  is  affirmation, 
is  merely  this.  In  all  denial  we  must  have  the  assertion  of  a 
positive  ground  ;  and  the  positive  ground  of  the  second  denial 
can  be  nothing  but  the  predicate  denied  by  the  first.  I  can 
not  say  "  It  is  false  that  A  is  not  b!'  unless  I  already  possess 
the  positive  knowledge  that  A  is  b.  And  the  reason  of  my 
incapacity  is  that  no  other  knowledge  is  a  sufficient  ground. 

§  30.  I  will  briefly  explain.  We  know  well  by  this  time 
that,  in  judging  A  not  to  be  b,  I  presuppose  a  quality  in  A  which 
is  exclusive  of  b.  Let  us  call  this  y.  I  now  desire  to  deny 
my  judgment,  and  need,  as  before,  some  quality  as  the  ground 
of  my  new  denial.  Let  us  take  some  quality  other  than  b. 
Let  this  quality  z  be  exclusive  of  y,  and  let  us  see  what  we 
have.  We  have  now  Az  with  the  exclusion  of  ^  which 
excluded  b.  But  that  leaves  us  nowhere.  We  can  not  tell 
now  if  A  is  b,  or  is  not  b,  because  z  itself,  for  anything  we  know, 


ISO  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

may  also  exclude  b,  just  as  much  as  j  did.  \A/hat,  in  short,  we 
have  got  is  our  own  private  impotence  to  deny  "  A  is  ^  ;  "  but 
what  we  want  is  an  objective  ground  for  declaring  such  a 
denial  to  be  false. 

The  same  result  holds  good  with  any  other  quality  we 
can  take,  excepting  b  itself  The  only  certainty  that  b  is  not 
absent  is  got  by  showing  that  b  is  present.  For  the  possible 
grounds  of  the  exclusion  oib  being  quite  indefinite,  you  cannot 
get  rid  of  them  by  trying  to  exhaust  the  negations  of  b.  You 
could  only  do  that  if  the  number  of  possibilities  with  respect 
to  A  had  already  been  limited  by  a  disjunctive  judgment. 
And  this  is  not  here  the  case. 

Suppose,  for  instance,  we  have  the  judgment  that "  Ultimate 
reality  is  not  knowable,"  and  we  wish  to  assert  that  this  judg- 
ment is  false.  We  expose  the  ground  on  which  it  is  based, 
and  go  on  to  show  that  this  ground  is  not  valid.  Our  pro- 
ceeding, no  doubt,  may  be  perfectly  admirable,  but  all  that  it 
gives  us  is  the  right  to  doubt  the  original  judgment,  and  to 
deny  the  truth  of  the  basis  it  stands  on.  If  we  wish  to  deny 
the  original  judgment,  we  can  not  do  that  by  refuting  our 
antagonists.  We  must  show  ourselves  that  reality  is  know- 
able.  The  ground  for  the  denial  of  "  A  is  not  b!'  must  lie  in 
"  A  is  br 

§  31.  I  will  endeavour  to  remove  a  possible  source  of 
misapprehension.  It  might  be  urged  that  in  practice  the 
denial  of  a  judgment  can  always  be  denied  by  something  other 
than  the  judgment  itself.  Thus,  for  instance,  "It  did  rain 
yesterday,"  may  be  false,  because  it  snowed  or  because  it  was 
fine.  But  each  of  these  can  be  denied  on  the  ground  of  the  other. 
The  result  of  our  double  negation  of  "  it  rained,'*  might  be 
either  "  it  snowed,"  or  again  "  it  was  fine  :  "  and  we  might  return 
to  "  it  rained,"  by  virtue  not  of  a  double  but  of  a  triple  denial. 

But  this  objection  would  rest  on  a  misunderstanding.  It  is 
'perfectly  true  that,  in  denying  "  it  rained,"  I  must  imply  and 
make  use  of  some  discrepant  quality.  It  is,  once  more,  true 
that  what  I  have  in  my  mind,  and  should  assign  as  my  reason, 
may  be  either  "  it  snowed  "  or  again  "  it  was  fine."  But  it  is 
a  mistake  to  conclude  that  the  denial  really  rests  upon  either 
the  one  of  these  or  the  other.     Whatever  you  might  have  had 


Chap.  V.]  DOUBLE   NEGATION.  15 1 

in  your  mind,  no  logic  could  force  you  to  allow  that  your 
denial  had  committed  you  to  either  "it  snowed"  or  "  it  was 
fine."  What  we  use  in  denial  is  not  the  whole  disparate :  it 
is  that  part  of  the  disparate  which  answers  our  purpose.  The 
denial  asserts  no  more  than  the  existence  of  so  much  quality 
as  is  enough  to  exclude  the  judgment  "it  rained."  This 
universal  "  so  much  "  is  possessed  by  either  "  it  snowed  "  or  "  it 
was  fine,"  and  this  you  can  not  banish  by  anything  short  of  the 
judgment  "it  rained."  In  other  words,  if  you  say  "it  did  not 
rain,"  you  are  at  once  committed  to  a  positive  "because,"  but 
you  are  committed  to  nothing  but  an  unspecified  quality.  The 
evidence  for  this  quality  no  doubt  in  the  end  must  be  found 
in  the  presence  of  a  contrary  assertion,  but  the  mere  con- 
tradiction does  not  affirm  this  or  any  particular  contrary.  It 
affirms  merely  ^^w^  contrary,  and  you  get  rid  of  this  only  by  the 
judgment  "it  did  rain."  We  find  here  once  more  the  constant 
ambiguity,  which  we  have  seen  (Chap.  III.  §  19)  makes  the 
use  of  negation  so  precarious.  It  is  so  difficult  to  work  with 
double  denial  that  I  hardly  can  expect  in  the  present  volume 
to  have  supplied  no  example  of  the  error  I  condemn.* 

*  Mr.  Venn,  I  think,  has  certainly  done  so.  When  I  had  the  pleasure 
of  reading  his  Sy77ibolic  Logic,  I  congratulated  myself  on  the  fact  that  I 
had  already  written  J;he  present  and  all  the  preceding  chapters.  I  have 
not  found  occasion  in  consequence  to  alter  anything  of  what  I  had 
written,  but  I  should  like  to  use  one  of  his  principal  doctrines  to  exemplify 
the  fallacious  use  of  the  negative.  I  have  added  this  discussion  as  a  mere 
appendix,  for  it  hardly  carries  the  subject  further.  It  is  due  to  myself  to 
defend  my  own  views  against  a  counter  theory  from  a  writer  of  established 
and  merited  reputation. 

After  calUng  attention  to  the  ambiguity  of  affirmative  uiyversals,  the 
doubt,  that  is,  if  they  affirm  the  existence  of  their  grammatical  subject,  Mr. 
Venn,  if  I  understand  him  rightly,  asserts  that  at  all  events  the  negative 
is  not  ambiguous  (p.  141).  I  will  not  here  enquire  if  in  other  places  he  is 
compelled  to  recognize  that  the  opposite  of  this  assumption  is  true.  At  all 
events  the  foundation  he  here  seems  to  build  on  is  the  assertion  that 
negatives  have  only  one  meaning.  "  It  comes  to  this  therefore  that  in 
respect  of  what  such  a  proposition  affirms  it  can  only  be  regarded  as 
conditional,  but  that  in  respect  of  what  it  denies  it  may  be  regarded  as 
absolute  "  ( 142).  The  affirmation  of  xy  is  always  ambiguous,  since  x  may 
not  be  actual;  but  the  denial  of  ,r  not-^  is  perfectly  clear.  And  upon  this 
basis  he  seems  to  build  his  doctrine. 

Now  the  reader  of  this  volume  will  know  that  a  negation  is  always 
ambiguous.     We  may  consider  this  as  settled,  and  I  will  not  re-discuss 


152  THE   PRINCIPLES   OF   LOGIC.  [Book   I 

the^eneral  question.  I  will  first  call  attention  to  the  seeming  absurdity 
of  ^r.  Venn's  doctrine.  He  teaches  in  effect  that,  although  you  do  not 
knowwhat  a  statement  means,  you  can  always  tell  what  you  mean  by 
denying  it.  )  And  he  ought  to  hold  that  the  ambiguity  of  a  judgment  at 
once  disappears,  if  you  deny  it  and  then  deny  your  denial.  This  course  has 
not  generally  been  found  so  successful. 

But  it  is  better  to  show  the  actual  mistake.  And  we  will  preface  our 
criticism  by  setting  down  some  elementary  truths.  You  can  not  argue  from 
the  assertion  of  possibility  to  the  assertion  of  actuality,  but  you  can  always 
argue  from  the  denial  of  possibility  to  the  denial  of  actuality.  To  deny 
possible  X  (you  must  of  course  not  take  "  possible ''  as  "  merely  possible  ")  is 
by  implication  to  deny  actual  x.  Now  the  simple  application  of  this  common- 
place doctrine  is  that,  if  you  are  given  a  connection  xy  and  do  not  know 
whether  it  is  possible  or  actual,  at  all  events,  if  you  deny  its  possibility, 
you  may  be  very  sure  that  you  also,  and  as  well,  have  denied  its  actuality. 
This  is  literally  (unless  I  misunderstand  him)  the  whole  principle  which 
Mr.  Venn  unconsciously  proceeds  upon,  and  the  idea  that  it  could  lead  to 
any  great  result,  or  to  a  better  understanding  of  hypothetical,  seems 
somewhat  strange. 

I  can  not  be  quite  sure  of  his  exact  procedure,  but  I  think  it  is  this. 
The  affirmative  judgment  both  affirms  and  denies.  Mr.  Venn  will  not 
say  that  what  it  affirms  is  mere  possibility,  but  he  quietly  assumes  that 
what  it  denies  is  impossibility.  (If  he  does  not  do  this,  he  makes  a  simpler 
mistake  to  which  I  will  return.)  That  is  to  say,  he  tacitly  and  without 
any  justification  assumes  that  x  not-j/  asserts  the  impossibility  of  xyj  and 
it  is  sole-y  by  denying  this  arbitrary  fixture  that  the  positive  xy  becomes 
unambiguous.  But  if  he  wishes  to  restrict  the  affirmative  judgment  to  the 
minimum  sufficient  to  deny  the  denial  of  possibihty,  surely  it  would  be 
better  to  say  ai  once,  "  The  affirmative  judgment  does  not  assert  more 
than  bare  possibihty."  He  would  so  have  done  openly  and  in  an  intelli- 
gible manner  the  very  thing  he  has  in  effect  done,  indirectly  and  most 
objectionably,,  by  going  round  through  two  denials.  The  procedure 
could  in  no  case  have  become  fnore  arbitrary. 

I  will  put  the  same  thing  otherwise.  With  affirmative  judgments 
possibility  is  the  minimum  :  with  negative  judgments  impossibihty  is 
the  maximum.  Now  it  is  uncertain  (we  may  so  interpret  Mr.  Venn)  if 
the  affirmative  xy  asserts  the  maximum  (actuality)  or  the  minimum 
(possibility),  but  it  is  certain  that  it  unambiguously  denies  the  negative. 
But,  if  the  negative  becomes  unambiguous  because  it  is  arbitrarily  fixed 
at  its  maximum  degree  (impossibility),  then  surely  it  is  clear  that  we 
thereby,  and  ipso  facto,  are  fixing  the  affirmative  at  its  minimum  degree. 
For  so  far  at  le^st  as  the  affirmative  denies  and  \'s,not  ambiguous,  it  is  so 
because  its  minimum  is  enough.  And  the  fallacy  is  simple.  This  minimum 
is  not  enough  unless  the  negative  is  fixed  at  the  maximum.  Suppose 
XioXrxy  to  mean  "  xy  does  not  exist,"  then  "  xy  is  possible '"  ceases  to  deny 
thi"  :  for,  although  xy  may  not  exist,  it  still  can  be  possible.  Again  \i  xy 
meant  "  xy  is  actual,"  then  "  xy  is  impossible  "  (or,  again,  "  if  ;irthen  no  j") 
is  not  its  contradictory,  and  goes  a  long  way  beyond  its  denial.  In  short, 
since  noi-xy  means  either  de  facto  non-existence  or  else  impossibility,  it 


Chap,  v.]  DOUBLE   NEGATION.  153 

seems  absurd  to  assert  that  the  denial  of  this  is  not  ambiguous.  And  if 
you  mean  to  fix  the  meaning  of  the  negative  arbitrarily,  it  seems  absurd 
to  shrink  from  doing  the  same  by  the  positive. 

In  conclusion,  if  we  suppose  that  not-xy  is  really  meant  to  assert  non- 
existence, that  is  to  deny  the  actuality  of  xy,  then  the  error  is  palpable. 
You  first  say  you  do  not  know  whether  xy  asserts  existence  or  possibihty, 
and  yet  you  say  it  denies  the  non-existence  of  xy.  But  possibility,  not 
affirming  existence,  of  course  can  not  deny  non-existence,  and  the  whole 
process  disappears  unless  you  rapidly  shuffle  from  one  term  to  the  other. 

This  hidden  equivocation  soon  begins  to  bear  fruit  in  the  curious 
reasoning  which  immediately  follows  (p.  143).  If  I  do  not  misapprehend 
Mr.  Venn,  he  tries  to  make  a  passage  from  bare  possibilities  to  a  positive 
existential  judgment.  I  confess  his  metaphysics  take  away  my  breath  ; 
and  I  am  bound  the  more  to  admire  his  audacity  as  he  somewhat  poses 
as  abjuring  "  transcendentalism,"  and  likes  to  take  things  "  in  a  perfectly 
matter  of  fact  way."  But  let  us  see  what  this  way  is.  We  suppose  four 
possibiHties,  (i)  x  with  j,  (ii)  x  not-_y,  (iii)  y  not-x,  and  (iv)  not-;r  not-_y. 
We  have  first  a  conditional  assertion  of  xy,  and  this  destroys  (ii).  We 
have  next  a  similar  assertion  of  yx^  and  this  destroys  (iii).  We  have 
therefore,  after  this  second  assertion,  but  two  possibilities,  (i)  and  (iv). 

"  Before,  the  positive  possibilities  were  three  in  number,  now  they  are 
reduced  to  two  ;  for  it  is  implied  that  everything  must  be  either  both  x 
and/  or  neither  of  the  two.  Carrying  this  process  one  step  further,  we 
see  that  three  such  "  [i.e.  conditional]  "  propositions  would  be  requisite  to 
establish  unequivocally  the  existence  of  any  one  of  the  four  classes.  If 
we  expunge  xy  "  [i.e.  not-.r  not-j/]  "  also,  we  are  then  reduced  at  last  to  an 
assertion  of  existence,  for  we  have  now  declared  that  xy  is  all,  viz. 
that  within  the  sphere  of  our  discussion  everything  is  both  x  and  y  " 

(P-  143). 

Now,  so  far  as  I  can  see,  we  may  understand  this  process  in  two 
different  ways,  but  on  either  understanding  the  argument  is  vicious.  The 
first  way  is  to  take  our  possibilities  as  holding  within  an  exhaustive 
disjunction.  As  Mr.  Venn  says,  we  know  "  that  everything  must  be  either 
xy,  or  X  not-_y,  or  y  not-;r,  or  not-x  not-j  "  (142).  The  disjunction  will 
rest  here  on  a  positive  existential  proposition,  and  the  inference  will  be 
quite  correct.  But  the  objection  is  that,  on  Mr.  Venn's  theory,  we  can 
hardly  assume  that  we  have  such  a  disjunction.  At  least  I  do  not  under- 
stand why  the  assertion.  Everything  is  one  of  four  possibilities,  should  be 
able  to  be  taken  in  its  positive  meaning.  We  surely  are  bound,  if  we 
wish  to  be  unambiguous,  to  take  it  as  denying.  And  if  you  take  it  as 
denying,  //  does  not  prove  the  conclusion.  It  asserts  that  what  is  not  one 
of  four  possibiHties  is  non-existent  (or  impossible),  but  it  does  not  say  that 
anything  exists.  ThQ  possibility  of  everything  is  all  that  is  asserted,  and 
from  this  the  argument  will  not  take  you  to  more  than  the  sole  possibility  of 
xy.  If  you  start  with  nothing  but  possibilities,  you  can  not  cross  from  a 
bare  possibility  to  actual  existence  simply  on  the  ground  that  the  other 
possibilities  have  sunk  into  nothingness.  At  least  I  am  sure  "tran- 
scendentalists "  especially  would  be  interested  in  learning  Mr.  Venn's 
"  matter  of  fact  way  "  of  accomplishing  this  exploit. 


154  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

We  thus  see  that  the  reasoning  can  not  be  based  on  an  affirmative 
existential  disjunction.  And  without  this  foundation  it  is  thoroughly 
unsound.  Not-;ir  not-j/  is  to  be  suppressed  by  a  conditional  judgment,  and 
in  its  dying  struggles  is  to  establish  xy  as  "  an  assertion  of  existence." 
I  will  not  ask  what  the  conditional  proposition  could  be.  "If  anything 
exists  then  xy  exists  "  might  answer  the  purpose  ;  but  it  would  not  do  so 
unless  it  were  really  unconditional,  and  covertly  contained  the  very 
assertion  that  "  xy  is  actual."  And  this  I  think  is  the  alternative  to  which 
we  are  brought:  we  either  completely  abandon  and  throw  over  our 
doctrine  of  the  superiority  of  the  negative,  and  avowedly  start  with  an 
affirmation  of  existence  :  or  else  we  prove  the  existence  of  xy  through  a 
double  denial  which  assumes  the  conclusion  in  order  to  extract  it. 

We  may  verify  the  presence  of  the  same  ambiguity  in  the  extraordinary 
assertion  that  contrary  judgments,  such  as  "  All  x  is-j  "  and  "  No  x  is  yP 
can  be  compatible  (145).  It  is  not  worth  while  to  enter  into  a  discussion 
of  this  matter.  They  are  of  course  compatible  if  you  allow  yourself  to 
play  on  their  ambiguity ;  but  how  in  that  case  they  can  be  said  to  be 
contrary  I  have  no  conception.  "  The  interesting  and  unexpected 
application  "  is  to  me,  1  confess,  not  anything  beyond  a  confused  example 
of  a  well  known  doctrine  concerning  the  relations  of  possibility  and 
existence.  But  I  confess  besides  that,  I  have  never  been  much  used  "  to 
discuss  the  question  in  a  perfectly  matter  of  fact  way." 

I  need  not  mention  what  seem  to  me  other  mistakes  of  much  the  same 
kind.  And,  beside  these,  there  are  some  statements  in  connection  with 
the  hypothetical  judgment  with  which  I  do  not  agree,  but  for  which,  I 
think,  my  treatment  of  the  subject  has  provided  sufficiently.  I  am  sorry  to 
be  forced,  both  here  and  again  (Chap.  VII.),  to  emphasize  my  difference 
with  Mr.  Venn.  And  by  way  of  compensation  I  should  like,  if  he  will 
allow  me,  to  offer  a  suggestion.  If  Mr.  Venn  had  not  such  a  horror  of 
"  metaphysics  "  and  "  transcendentalism,"  if  he  was  a  little  less  resolved 
to  be  "  matter  of  fact,"  and  "  discuss  the  question  entirely  on  scientific  or 
logical  ground,"  I  fancy  he  would  have  come  somewhat  nearer  a  solution 
of  the  problems  it  is  his  merit  to  have  undertaken.  At  any  rate  I 
suspect  his  idea  of  science  might  have  been  expanded,  and  some 
prejudices  as  to  "  matter  of  fact "  have  been  somewhat  loosened.  He 
would  certainly  have  imbibed  a  dislike  for  artifices,  and  such  a  scruple 
against  entertaining  commodious  fictions,  as  in  itself  would  have  saved 
him  from  a  succession  of  serious  logical  mistakes. 


(     155    ) 


CHAPTER  VI. 

THE   QUANTITY  OF  JUDGMENTS. 

§  I.  If  in  considering  an  idea  you  attend  to  its  content,  you 
have  its  intension  or  comprehension.  Its  extension  may  be 
taken  in  two  different  senses.  It  is  an  instance  or  instances, 
ideal  or  actual.  It  refers  ultimately  to  the  real,  but  it  may 
directly  signify  {a)  any  other  more  concrete  idea  which  contains 
the  intension,  or  (b)  any  individual  of  which  the  intension  can  be 
predicated.  Thus  if  "  horse  "  signifies  the  attributes  possessed 
by  a  horse,  it  is  taken  in  intension.  If  it  signifies  any  other 
idea  which  includes  "  horse,"  e.g.  cart-horse  or  race-horse,  it  is 
taken  in  extension.  And  again,  it  is  otherwise  taken  in  exten- 
sion if  it  is  used  for  individual  horses.* 

§  2.  We  have  come  again  upon  a  distinction  which  is  now 
familiar.  An  idea  is  symbolic,  and  in  every  symbol  we  separate' 
what  it  means  from  that  which  it  stands  for.  A  sign  indicates 
or  points  to  something  other  than  itself;  and  it  does  this  by 
conveying,  artificially  or  naturally,  those  attributes  of  the  thing 
by  which  we  recognize  it.  A  word,  we  may  say,  never  quite 
means  what  it  stands  for  or  stands  for  what  it  means.  For 
the  qualities  of  the  fact,  by  which  it  is  recognized  and  which 
correspond  to  the  content  of  the  sign,  are  not  the  fact  itself. 
Even  with  abstracts  the  actual  case  of  the  quality  is  hardly 
nothing  'but  the  quality  itself.  The  idea  and  the  reality  are 
presumed  to  be  different. 

It  is  perhaps  an  ideal  we  secretly  cherish,  that  words 
should  mean  what  they  stand  for  and  stand  for  what  they 
mean.  And  in  metaphysics  we  should  be  forced  to  consider 
seriously  the  claim  of  this  ideal.  But  for  logical  purposes  it  is 
better  to  ignore  it.  It  is  better  to  assume  that  the  meaning  is 
other  than  the  fact  of  which  the  meaning  is  true.  The  fact  is 
anjndividual  or  individuals,  and  the  idea  itself  is  an  universal, 
"fhe  extension  can  not  be  reduced  to  intension^ 

*  If  it  were  used  iox  possible  horses,  it  would  be  taken  in  sense  {a).  Cf, 
pp.  158,  167,  173- 


1 56  THE  PRINCIPLES   OF  LOGIC.  [Book  L 

§  3.  The  difference  may  be  expressed  by  the  terms 
"  denotation  "  and  "  connotation."  These  phrases  have  found 
favour  with  the  English  public,  and  the  indiscriminate  use  of 
"  connotation  "  marks  one  kind  of  superior  person.  But  they 
serve  no  usefuk  purpose  in  logic.  They  are  unnecessary  and 
objectionable.  They  have  no  advantage  over  the  terms  in 
general  use,  and  they  have  in  addition  a  positive  vice.  To 
"  connote  "  is  to  "  imply  ;  "  and  the  meaning  of  a  word  is  not 
its  implication.  With  the  names  of  individuals  the  meaning 
may  perhaps  be  said  to  be  "connoted,"  but  with  adjectives 
such  as  "red,"  and  abstracts  such  as  "redness,"  what  is 
"  connoted "  is  clearly  not  at  all  the  attributes  but  the 
individual  reality.  Nothing  but  ambiguity  can  arise  from 
such  perversions.  If  you  will  use  a  word  which  signifies 
implication,  to  convey  what  more  usually  is  the  direct 
meaning,  you  must  expect  the  confusion  which  your  unfor- 
tunate choice  has  already  to  some  extent  occasi6ned. 

§  4.  Hand  in  hand  with  this  slovenly  terminology  there 
goes  a  ^uperstition  we  have  in  part  refuted  (Chap.  II.  §  17). 
We  are  told  that  words  may  be  "  non-connotative."  They 
may  signify,  we  are  told,  a  subject  only  or  only  an  attribute. 
Both  of  these  assertions  must  be  rejected.  No  word  such  as 
"  whiteness  "  stands  simply  and  solely  for  the  abstract  quality.* 
It  means  this  directly  ;  but  it  indirectly  points  to  an  implied 
individual,  an  actual  case  of  whiteness.  And  still  less  can  be 
said  for  the  doctrine  we  have  already  refuted.  The  name  of 
an  individual  must  carry  with  it  and  imply  certain  attributes, 
or  else  its  attachment  to  that  individual  becomes  a  psycho- 
logical impossibility.  It  is  mere  want  of  thought  which 
allows  us  to  suppose  that  a  sign  can  mean  nothing  and  yet 
stand  for  something. 

§  5.  It  would  be  as  easy  to  prove  that  a  word  may  mean 
nothing  and  may  also  stand  for  nothing.  And  it  may  be 
useful,  perhaps,  at  this  point  to  digress.  We  have  seen  that 
all  propositions  are  "  real  "  (p.  41).  Verbal  propositions  become 
manifestly  real,  if  you  write  them  "  The  meaning  of  S  is  P." 

*  All  ideas  imply  a  reference  of  their  content  to  the  real  (p.  4),  and 
hence  to  the  individual.  We  may  notice  besides  that  abstracts  imply 
within  their  content  a  supporting  subject.     They  are  doubly  adjectival. 


Chap.  VL]  THE   QUANTITY  OF  JUDGMENTS.  157 

But  there  is  a  class  of  judgments  where  the  subject  has  got  no 
definite  meaning,  and  is  not  a  perfect  sign.  If  we  take  such 
a  statement  as  "  magistri  is  the  genitive  case  of  magister^'  we 
might  be  tempted  to  assert  that  some  words  are  devoid  of 
both  extension  and  intension. 

"Theophilus  is  Greek,"  "Theophilus  is  dear  to  God," 
"  Theophilus  has  the  measles."  The  last  of  these  informs  us 
of  the  disease  of  a  man.  The  second  tells  us  the  meaning  of 
a  name.  The  first  assures  us  that  a  word  is  a  member  in  a 
system  of  signs,  but  it  seems  to  give  us  nothing  which  that 
word  stands  for  and  nothing  that  it  means.  If  a  sign  were 
something  with  a  definite  signification,  then  we  could  not  say- 
that  all  words  are  signs.  We  may  know  of  a  sound  no  more 
than  this,  that  it  is  a  sign.  It  stands  for  something,  but  we 
do  not  know  what ;  and  it  means  something  also,  but  what  we 
do  not  know. 

I  ^And  we  are  not  at  the  end.  This  last  remnant  of  ordinary 
extension  and  intension  is  doomed  to  vanish.  I  may  treat  the 
word  as  a  common  noise.  "  Why  did  you  make  that  noise 
Theophihts  when  you  saw  that  man  }  Theophilus  is  not  a 
^pleasant  sound."  We  have  here  no  signification  and  no 
meaning,  nor  have  we  any  longer  a  word.  But  even  here 
in  a  rudimentary  form  we  have  the  sides  of  extension  and 
intension.  We  may  distinguish  two  elements  that  are  blended 
in  Theophilus.  Even  here  it  is  universal,  and  is  the  product 
of  abstraction  and  generalization.  The  sound  that  I  should 
know  under  all  its  differences,  of  varying  tone,  of  the  person 
uttering,  and  of  places  and  times,  is  one  side  of  the  whole. 
The  other  is  this  particular  utterance  and  other  possible 
particular  utterances.  The  elements  still  co-exist  at  this  early 
stage  of  their  evolution.     We  can  never  separate  the  one  from 

j^the  other  except  by  a  mistake. 

§  6.  Let  us  dismiss  for  ever  the  term  "connotation,"  and 
try  to  keep  clear  of  the  errors  it  beacons.  We  may  pass  to  a 
doctrine  of  another  kind,  not  so  misleading  but  equally  idle. 
Extension  and  intension,  we  are  told,  are  related  and  must  be 
related  in  a  certain  way.  The  less  you  happen  to  have  of 
the  one,  the  more  you  therefore  must  have  of  the  other. 
This  statement  has  often  passed  itself  off  as  both  true  and 


158  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

important.  I  confess  that  to  me  it  has  always  seemed  either 
false  or  frivolous. 

{a)  If  we  take  extension  to  mean  that  number  of  real 
individuals  of  which  the  meaning  is  true,  then  it  is  ludicrously- 
false  that  an  increase  of  the  extension  is  a  decrease  of  the 
meaning.  The  logician  who,  impelled  by  the  practical  syl- 
logism, begets  a  child,  does  not  find  his  doctrine  verified  by 
the  fact.  The  conclusion,  which  appears  from  the  union  of 
the  premises,  no  doubt  may  surprise  him  and  add  to  his 
experiences,  but  it  may  not  diminish  the  "comprehension" 
with  which  he  hears  the  word  child.  His  new-born  instance 
may  destroy  his  definition  of  the  genus  homo  as  animal  risibile^ 
but  the  content  it  shears  off  will  be  largely  made  good  by 
other  attributes.  He  may  say,  what  he  never  thought  to  have 
said,  A II  children  are  scourges. 

\  It  is  obvious  that  fresh  instances  may  increase  the  inten- 
sion by  the  discovery  of  attributes  essential  but  overlooked. 
The  doctrine  understood  in  this  sense  is  false.  And  if  you  write 
"  possible  "  for  "  actual  "  individuals,  still  diminution  of  the 
meaning  need  not  add  to  the  number.  If  possible  means  that 
which  is  presumed  to  exist,  we  may  remark  that  the  complex 
may  be  possible  in  fact  just  as  much  as  the  simple  ;  the  simple 
indeed  by  itself  may  be  impossible.  But  if  possible  means 
what  can  be  produced  by  artificial  and  arbitrary  thinking 
(p.  187),  we  have  now  obviously  left  the  sense  of  extension 
we  have  been  dealing  with.  The  extension  has  ceased  to 
lie  in  the  individuals  ;  it  has  become  those  groups  of  attributes 
in  which  analysis  can  find  the  meaning. 

§  7.  But  {b)  even  if  we  give  this  sense  to  extension,  the 
doctrine  is  not  true.  If  you  compare  ideas,  the  narrower 
meaning  does  not  always  have  the  wider  application.  Take 
a  simple  instance.  The  idea  of  the  visible  has,  we  may  all 
admit,  a  fuller  meaning  than  the  ideas  of  that  which  can  be 
tasted  or  smelt.  But  the  latter  have  not  got  any  greater 
extension.  Everywhere,  if  you  take  adjectives  or  combinations 
of  adjectives,  which  are  co-ordinate  and  which  can  not  be  sub- 
sumed the  one  under  the  other,  the  doctrine  ceases  to  have  any 
bearing.  Since  the  greater  emptiness  has  not  been  got  by 
further  abstraction,  there  is  no  reason  why  the  adjective  which 


Ohap.  VI.]  THE   QUANTITY   OF  JUDGMENTS.  1 59 

has  less  content  should  be  predicable  of  a  greater  number 
of  kinds. 

And  if  for  marks  and  combinations  of  marks  we  substitute 
laws  or  modes  of  combination,  the  same  thing  holds  good.  If 
these  laws  do  not  stand  the  one  under  the  other,  but  simply 
fall  under  a  common  head,  then  you  have  no  right,  on 
comparing  these  laws,  to  expect  the  emptier  to  be  the  more 
wide  and  the  wider  to  be  more  empty. 

§  8.  There  undoubtedly  is  some  truth  in  the  doctrine,  but 
that  truth  does  not  come  to  much  more  than  this.  If  you  take 
adjectival  marks  or  laws,  and  choose  to  arrange  them  in  the 
form  of  a  pyramid  ;  if  you  place  at  the  bottom,  and  as  the 
stones  of  your  lowest  layer,  all  those  ideas  which  have  nothing 
subordinate ;  if  you  form  the  second  and  superimposed  layer 
by  subtracting  the  differences  from  two  of  these  stones,  and 
by  placing  the  residue  left  by  the  operation  on  the  top  of  the 
pair ;  and  if  you  so  proceed  to  pile  layer  upon  layer,  so  as  to 
form  a  mass  which  grows  narrower  with  each  tier — if  all  this 
is  done,  then  it  is  geometrically  true  that  the  higher  you  go 
up  the  fewer  stones  you  will  find,  and  the  lower  you  go  down 
the  more  stones  you  will  have.  And  since  you  have  gone  up 
by  leaving  out  differences,  it  is  obvious  that  the  narrower  the 
pyramid  becomes  the  more  stones  will  each  single  stone  have 
to  stand  upon,  and  the  more  there  will  be  of  which  it  can  be 
predicated.  This  is  undeniable,  but  what  does  it  come  to } 
It  comes  to  this,  that  if  you  arrange  your  material  in  a 
certain  geometrical  figure,  then  it  will  have  certain  geo- 
metrical properties.  That  is  true,  but  it  seems  to  me  quite 
frivolous. 

§  9.  It  is  true,  I  admit,  that  if  B  must  be  C,  then,  supposing 
A  should  ever  be  B,  it  will  also  be  C.  But,  if  you  offer  me 
this  as  a  truth  about  A,  I  can  hardly  affect  to  feel  very 
grateful.  It  looks  to  me  more  like  a  truth  about  B.  You 
begin  to  establish  a  claim  to  gratitude  when  you  show  me 
also  that  A  is  B,  or  is  likely  to  become  so.  And  this  is  the 
real  question  at  issue.  If  you  arrange  ideas  in  a  certain  way 
they  will  have  the  qualities  of  that  arrangement.  Who  doubts 
it }  What  first  may  be  doubted  is  the  possibility  of  so 
arranging  all  ideas  ;  and  what  may  next  be  doubted  is  the 


l6o  THE   PRINCIPLES   OP'   LOGIC.  tBooK  1, 

wisdom  of  the  arrangement.  If  it  is  not  the  natural  relation 
of  the  material,  if  it  is  forced  and  arbitrary,  then  the  truth 
you  offer  me  may  after  all  be  sterile.  It  may  have  little  or 
nothing  to  do  with  the  actual  matter  in  hand. 

If  you  confine  yourself  to  the  ideas  of  adjectivals,  then 
(though  I  will  not  undertake  to  maintain  it)  I  think  that  with 
more  or  less  of  regularity  you  may  effect  your  pyramidal 
arrangement ;  but  I  think  you  much  over-estimate  its  value. 
If  reasoning  were  always  the  subsumption  of  a  stone  on  a 
lower  tier  under  a  stone  belonging  to  a  higher  layer,  then 
your  construction  would  begin  to  serve  as  a  machine  and  would 
even  live  ;  your  ladder  would  grow  green  and  blossom  as  the 
tree,  not  of  pedantry,  but  of  knowledge.  But  reasoning  is 
really  not  always  subsumption,  and  with  the  cutting  off  that 
root  of  delusion  your  tree  shows  dead,  and  breaks  before  the 
breath  of  actual  existence.  The  importance  ascribed  to  your 
arrangement  of  ideas  comes  from  a  fundamental  mistake. 
(See  Book  II.  Part  I.  Chap.  II.) 

§  lo.  And  there  remains  an  objection  we  can  not  discuss 
but  must  not  pass  over.  If  you  do  not  confine  yourself  to 
the  ideas  of  adjectives  and  their  combinations,  what  then } 
Take  ideas  of  individuals.  If  you  have  ideas  of  smaller 
wholes,  enclosed  in  and  subordinated  to  larger  wholes,  will 
it  there  be  true  that  the  wider  the  synthesis  the  emptier  it 
becomes  ?  Are  universals  always  more  abstract  than  particu- 
lars .?  Is  it  certain  that  the  idea  of  a  state  has  less  content 
than  the  idea  of  any  one  of  its  citizens  ?  Are  we  sure  that 
the  soul  is  more  of  an  abstraction  than  any  particular 
psychical  event  ?  Is  the  idea  of  God  assuredly  less  full  than 
the  idea  of  a  molecule }  And  if  we  consider  the  idea  of 
synthetical  unity,  it  does  not  appear  that  the  higher  and  wider 
function  of  synthesis  need  have  less  attributes  than  a  sub- 
ordinate function.  If  we  entertain  the  belief  that  syntheses 
are  possible  which  are  not  the  abstraction  from  lower  syn- 
theses, but  are  the  individuations  of  these  lower  abstractions, 
then  the  doctrine  which  has  showed  itself  to  be  idle  once 
more  becomes  a  positive  error. 

This  objection,  I  am  aware,  will  not  press  very  heavily. 
There  are  few  readers  not  so  wise  in  their  own  esteem  as  to 


Chap.  VI.]  THE   QUANTITY   OF  JUDGMENTS.  l6l 

convict  this  suggestion  of  folly  or  madness.  It  would  belong  to 
metaphysics  to  lay  folly  at  the  door  of  its  true  possessors.  It 
is  sufficient  here  for  our  logical  purpose  to  have  pointed  out  an 
objection,  disregarded  and  despised,  but  in  itself  not  despicable. 
Apart  from  this  possible  ground  of  dissent,  and  confining 
ourselves  to  the  consideration  of  marks  and  the  modes  of 
their  union,  we  may  sum  the  matter  so.  The  law  of  the 
relation  of  extent  to  intent  is  not  a  law  of  ideas  themselves  ; 
it  is  a  law  of  pyramidal  arrangement  ;  and  that  arrangement 
in  the  case  of  ideas,  where  it  is  possible,  is  not  of  importance. 
It  may  fairly  be  relegated  to  our  logical  lumber-room. 

§  II.  The  question  which  is  next  to  claim  our  notice  is 
still  concerned  with  Extension  and  Intension.  If  we  leave 
mere  ideas  and  go  on  to  judgments,  it  has  been  asked 
whether  these  make  a  statement  in  respect  of  the  extension  of 
their  elements,  or  the  intension,  or  both.  And  this  is  a  topic 
we  can  not  quite  pass  over,  as  it  presents  us  with  several 
dangerous  illusions.  I  will  begin  by  the  assertion  that  every 
proposition  can  be  read  in  whichever  of  these  ways  we  prefer. 
I  will  then  show,  in  the  first  place,  how  all  can  be  interpreted 
in  extension,  and  will  prove  the  same,  secondly,  with  respect 
to  intensjon.    ) 

§  i2VEvery  judgment  makes  a  double  affirmation,  or  a 
single  affirmation  which  has  two  sides.  It  asserts  a  con- 
nection of  dififerent  attributes,  with  an  indirect  reference  to  an 
identical  subject ;  or  it  directly  asserts  the  identity  of  the 
subject,  with  an  implication  of  the  difference  of  its  attributes. 
If  you  prefer  to  consider  the  identity  of  the  subject  (im- 
mediate or  ultimate),  you  read  the  judgment  in  extension. 
If  again  you  emphasize  the  connection  of  the  differences, 
you  take  the  judgment  intensionally.  It  is  not  true  that 
every  judgment  is  naturally  read  in  both  of  these  ways. 
It  is  true  that  all  judgments  can  be  read  correctly  in  either 
manner,  and  read  legitimately.     ' 

If  you  take  the  proposition  "  Dogs  are  mammals,"  then 
this  means  either  that,  where  anything  is  a  dog,  the  same 
individual  thing  will  be  a  mammal  ;  or  that,  given  in  anything 
the  attribute  dog,  you  will  certainly  have  with  it  the  attribute 

M 


1 62  THE  PRINCIPLES  OF   LOGIC.  [Book  L 

mammal.  And  it  is  possible  to  interpret  every  judgment  in 
this  self-same  way7~l 

§  13.  Dismissin'g  for  the  present  the  intensional  reading, 
let  us  consider  interpretation  in  Extension.  We  find  here  the 
presence  of  misleading  errors.  It  is  a  common  doctrine  that 
when  we  read  in  extension  we  assert  inclusion  in  a  class  or 
collection.  We  are  told  that  in  "Dogs  are  mammals" 
no  attribute  is  really  affirmed  of  dogs  ;  the  assertion  is  that 
the  things  called  dogs  are  included  within  the  class  of 
mammals.  I  can  discover  little  in  this  current  theory  but 
error  and  confusion. 

It  sounds  at  least  palpable,  when  we  hear  of  enclosing 
within  a  class.  But  try  to  handle  it,  and  at  once  your  grasp 
is  closed  upon  mist  and  unreality.  The  class,  if  it  is  to  be 
real  at  all,  must  be,  I  presume,  an  aggregate  or  collection  of 
individuals ;  and  this  must  exist  either  in  my  head  or  else 
outside  it.  The  latter  alternative  can  hardly  be  meant. 
There  is  no  actual  physical  aggregation  which  answers  to 
every  general  name.  For  every  single  mark  would  be  the 
ground  of  such  an  aggregate,  and  I  can  not  suppose  that 
any  one  believes  that  these  strange  complications  of  groups 
or  herds  actually  exist  in  rerum  natnra. 

§  14.  "  The  class  is  mental.  It  is  no  group  of  things.  It 
is  our  own  private  way  of  putting  images  together  within  our 
"own  minds."  But,  at  the  risk  of  seeming  to  affect  singularity, 
I  am  bound  to  assert  that  within  my  own  mind  I  can  not  find 
these  classes.  By  a  class  I  suppose  you  mean  a  group  of 
images  which  actually  exist ;  but  when  I  come  to  the  facts 
and  look  into  my  mind,  and  survey  what  is  there  when  I  hear 
the  word  "  mammals  "  or  "  triangles "  or  "  cats,"  I  scarcely 
ever  am  able  to  find  an  actual  group.  The  idea  that 
"  mammals "  is  the  name  of  a  flock  of  mammal-images, 
herded  together  in  my  mental  field,  and  that  among  these  I 
can  see  the  little  pack  of  dogs,  and  all  the  cats  sitting 
together,  and  the  rats,  and  the  rabbits,  as  well  as  the 
elephants,  all  marked  with  curious  references  and  cross- 
references  to  heads  "  quadruped  "  and  "  carnivorous  "  and 
"  placental "  and  Heaven  knows  what  else — I  do  not  think 
that  this  looks  like  the  fact. 


Chap.  VI.]  THE   QUANTITY   OF  JUDGMENTS.  163 

§  15.  These  flocks  and  herds  are  pure  mythology,  they  are 
nothing  real.  But  let  us  suppose  that  they  really  exist. 
Entertaining  fables,  we  may  unawares  embrace  a  truth.  Let 
*■  mammals  "  be  a  group  of  mammal-images  ;  and  let  "  dogs  " 
be  a  mental  pack  of  dog-images  ;  and  let^the  judgment  "  Dogs 
are  mammals"  be  the  inclusion  of  the  former  within  the 
latter.     But  what  does  this  mean  .? 

If  I  look  at  the  mammals  I  either  know  which  mammals 
are  dogs,  or  this  is  hid  from  me.  {a)  Suppose  that  I  know  it. 
The  inclusion  then  means  that  a  certain  definite  number  of 
my  present  mammal-images  are  also  dogs,  and  that  these  are 
surrounded  or  mixed  up  with  the  residue  of  mammal-images 
which  are  not  dogs.  The  judgment  asserts  a  spatial  relation 
in  my  mind  of  the  dog-mammals  to  the  mammals  which  are 
rats  and  cats  and  rabbits  and  the  rest.  But  such  juxta-position, 
let  it  be  ever  so  actual  in  my  imagination,  is  clearly  not  what 
we  meant  by  our  judgment.  I  wanted  to  say  sorpething  real 
about  dogs  ;  but  this  local  relation  fabled  in  my  head  does 
not  even  pretend  to  represent  external  existence. 

{b)  And  if  I  do  not  know  which  mammals  are  dogs,  the 
case  is  not  altered.  I  regard  my  mental  conglomeration  of 
mammals,  and  fail  to  distinguish  the  dogs  from  the  cats.  I 
can  not  say  which  image  is  a  dog-image,  but  I  know  that  the 
dogs  are  every  one  there.  They  are  inside  the  mammal-fold 
and  not  outside.  The  mammals  range  over  a  mental  park, 
and  all  the  dogs  are  on  this  side  of  the  paling.  But  that 
again  is  not  what  I  meant  to  assert.  The  local  position  of 
my  canine  images  with  respect  to  the  enclosure  which 
bounds  my  mammals,  is  not  the  idea  which  I  meant  to 
convey  by  "  Dogs  are  mammals." 

§  16.  These  interpretations  are  fictions — that  is  one  objec- 
tion. But  it  is  followed  by  another — they  are  unprofitable 
fictions.  They  are  not  only  baseless  :  they  also  are  useless. 
They  do  not  read  the  whole  proposition  in  extension.'  If  the 
extension  means  the  objects  called  mammals,  then  in  neither 
case  is  "  mammals,"  in  this  sense,  the  predicate.  In  saying 
"  Dogs  are  enclosed  by  mammals,"  I  do  not  say  that  "  Dogs 
are  mammals."  A  group  of  objects  is  one  thing  ;  a  spatial 
relation,  indefinite  or   definite,  to  that   group   of  objects    is 

M  2 


l64  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

clearly  another  thing.  And,  what  is  more,  that  relation  is  an 
attribute  of  dogs.  The  local  relation  is  not  the  things  them- 
selves, and  it  certainly  is  predicated  as  qualifying  dogs.*  If 
the  ostensible  predicate  has  been  taken  in  extension,  the 
proposition  has  in  part  been  read  intensionally  ;  for  it  has 
asserted  an  attribute  of  the  subject.  The  inclusion  within  the 
class  has  no  meaning,  if  the  class  is  the  mere  individuals 
themselves,  and  the  copula  simply  asserts  them  of  the  subject. 
But  if  the  judgment  affirms  a  spatial  relation  to  some  of  those 
individuals,  or  the  area  they  all  occupy,  or  the  fence  that 
confines  them,  then  what  the  judgment  really  affirms  is  an 
attribute. 

§  17.  If  we  keep  to  extension  we  must  keep  to  the  objects, 
and  it  is  these  we  must  try  to  predicate  of  the  subject.  In 
"  Dogs  are  mammals  "  we  must  try  to  assert  "  some  mammals  " 
of  dogs.  What  is  affirmed  must  be  identity.  The  dogs  and 
dog-mammals  are  all  the  same  thing.     (Cf.  Chap.  I.  §  17.) 

If  they  were  wholly  the  same  there  would  be  no  difference. 
They  could  not  then  be  at  all  distinguished,  and  both  sides 
of  the  judgment  would  fall  together.  The  judgment  would 
disappear.  Hence  a  difference  must  exist ;  and  what  we 
mean  to  say  must  come  to  this,  that,  Though  the  dogs 
and  dog-mammals  are  the  same,  yet  for  all  that — what  ? 
Here  we  have  to  join  issue. 

For  all  that,  we  may  say,  they  are  sometimes  inside  the/ 
mammal-enclosure  and  sometimes  outside,  and  that  is  the 
difference.  The  dog-mammals  sometimes  are  packed  by 
themselves,  and  go  wandering  off  in  the  mental  distance, 
.  and  at  other  times  their  images,  compelled  by  some  secret 
influence,  consort  with  all  whose  blood  flows  warmly.  But 
•  this  strange  mythology  would  not  answer  to  our  meaning. 
We  never  intended  to  say  that  the  dogs  could  exist  indiffer- 
ently on  each  side  of  a  hedge  which  grows  in  our  minds. 

§  18.  "The  dog-mammals  and  the  dogs  are  all  the  same, 
and  yet  for  all  that  their  names  are  different.  You  have  a 
set  of  individuals  which  obviously  in  themselves  are  simply 
themselves.     The  difference  asserted  is  the  difference  of  their 

*  I  do  not  say  the  spatial  relation  of  A  to  B  is  nothing  but  an  attribute 
of  A.     Still  it  is  such  an  attribute. 


Chap.  VI.]  THE  QUANTITY  OF  JUDGMENTS.  1 65 

two  signs  *  mammal '  and  '  dog.'  That  surely  is  a  very  palpable 
thing,  and,  in  saying  '  Dogs  are  mammals,'  we  mean  to  assert 
that  certain  definite  indivisible  objects  have  got  two  names. 
It  happens  that  they  have  been  christened  twice,  or  christened 
with  two  names,  and  this  is  the  real  heart  of  your  mystery." 

The  explanation  possesses  the  merit  of  simplicity.  It  is 
perhaps  too  simple  for  sophisticated  mortals.  Belief  in  it  will 
not  "  come  with  observation,"  but  demands  a  new  birth  from 
the  world  of  fact  into  the  world  of  faith.  Philosophy  has  not 
revealed  it,  and  not  many  wise  are  likely  to  accept  it.  The 
creed  of  nominalism  is  no  theme  for  argument.  To  those 
who  believe  that  assertions  about  things  assert  nothing  but 
names,  the  universe  has  long  ago  given  up  her  secrets,  and 
given  up  everything. 

§  19.  The  first  interpretation  asserts  that  the  individuals, 
notwithstanding  their  sameness,  cross  and  recross  the  mam- 
mal-fence. The  second  asserts  that,  although  they  are  the 
same,  their  names  are  different.  The  first  interpretation  is  a 
fiction  ;  the  second  ignores  the  fact  to  be  interpreted.  Neither 
expresses  the  meaning  of  the  judgment ;  and  both  in  the  end 
do  predicate  attributes.  The  change  of  position  with  respect 
to  a  herd  or  the  pale  that  encloses  it,  is  a  spatial  attribute. 
The  possession  of  one  or  two  or  three  names  is  again  an 
attribute.  The  subject  is  not  two  different  names  ;  it  /las 
them.  One  name  ts  not  the  other  ;  it  co-exists  with  it.  One 
thing  as  distinguished  is  not  the  other  thing  ;  both  have  a 
quality  which  is  the  same.  On  the  nominalist  interpretation 
the  actual  predicate  is  not  taken  in  extension.  The  interpre- 
tation is  not  only  ludicrously  false,  but,  if  we  take  it  as  true,  it 
still  asserts  an  attribute  of  the  subject. 

The  natural  and  the  true  interpretation  of  "Dogs  are 
mammals "  is  that  dog  and  mammal  are  different  attributes, 
and  that  these  differences  co-exist  within  the  same  things  ;  or 
again,  that,  though  the  things  are  certainly  the  same,  for  all 
that  they  possess  two  different  attributes,  dog  and  mammal. 
But  this  natural  interpretation  involves  the  abandonment  of 
the  theory  of  inclusion  within  the  predicate. 

§  20.  And  if  you  understand  extension  in  a  different  sense, 
the  result  is  the  same.     The  class  of  mammal  may  be  taken 


1 66  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

to  contain,  not.  only  the  collection  of  individuals  which  are 
mammals,  but  also  the  kinds  of  thing  which  are  mammal. 
"  Dog  is  one  kind,  and  the  judgment  includes  it  among  all  the 
other  kinds."  It  is  doubtful  what  this  means,  but,  whatever 
it  means,  the  extension  is  not  affirmed  as  a  predicate.  If  I 
have  in  my  mind  a  known  or  unknown  aggregate  of  kinds, 
and  say  that  dog  is  in  the  midst  of  this  aggregate,  then  I 
assert  of  dog  a  spatial  relation  to  a  set  of  elements  or  the  area 
they  occupy.  But  this  relation  is  surely  an  attribute.  If 
again  I  mean  that  dog  is  an  unit  which,  taken  in  addition 
with  other  units,  amounts  to  the  sum  which  I  call  "  mammal," 
then  I  assert  a  relation  to  the  other  units,  and  a  further 
attribute  that  results  from  this  relation.  If  I  mean  that  dog 
possesses  mammal,  and  that  other  kinds,  known  or  unknown, 
do  so,  or  that  dog  is  like  these  other  kinds  in  possessing 
mammal,  then  again  I  assert  an  attribute  of  dog,  the  having 
an  attribute,  and  the  identity  in  this  respect  with  some 
other  kinds. 

These  interpretations  are  all  forced  and  unnatural.  They 
none  of  them  are  really  what  I  have  in  my  mind  when  I  say 
"  Dogs  are  mammals."  Inclusion  is  not  what  I  mean  to 
assert.  But,  if  I  assert  it,  then  my  predicate  is  an  attribute. 
The  whole  or  part  of  the  extension  of  mammals  is  not  the 
real  predicate.  The  predicate  is  that  which  I  either  affirm  or 
deny  of  the  subject,  and  a  thing  is  not  the  same  as  a  relation 
between  itself  and  something  else. 

§  21.  If  you  say,  "The  dogs,  with  other  things,  make  up  a 
certain  amount  we  know  as  mammals,"  then  this  contribution 
to  a  certain  number  is  an  undeniable  attribute.  If  you  say, 
"The  dogs  share  a  quality  mammal  with  a  heap  of  other 
things,"  this  again  is  an  attribute.  If  you  suppose  dogs  and 
mammals  to  be  two  different  lots  in  two  adjoining  folds,  and 
if  you  pull  up  the  mental  hurdles  which  separate  them,  then 
you  can  not  say,  "  The  dogs  are  in  the  mammals,"  unless  you 
are  prepared  to  embrace  a  marsupial  or  some  other  such 
hypothesis.  They  are  related  locally  to  the  other  mammals  or 
to  the  area  or  fence  within  which  all  mammals  are  circum- 
scribed.    And  this  local  relation  is  an  attributive  predicate. 

The  mythology  you  invoke  is  not  strong  enough  to  save 


CiiAP.  VI.]  THE   QUANTITY   OF  JUDGMENTS.  167 

you,  and,  if  you  throw  yourself  into  the  arms  of  Nominalism, 
then  you  have  not  only  an  account  of  the  fact  which  is 
absurdly  insufficient,  but  the  difference  of  names  is  still  an 
attribute. 

And  if,  in  the  end,  to  escape  from  your  difficulties,  you  say 
"  The  class  is  no  real  collection  in  my  head  or  out  of  it.  It 
is  a  name  that  stands  for  the  possible  objects  that  have  a 
certain  attribute,"  then  the  answer  is  simple.  If  the  class  is  no 
longer  an  aggregate  or  collection,  it  has  become  little  else  than 
a  mere  description.  "  Dogs  are  included  in  a  possible  group  of 
things  which  are  mammals,"  "  Dogs  are  of  the  description 
mammal,"  "  Dogs  possess  the  attribute  mammal  " — what  is  the 
difference  between  these  three  assertions  }  I  ask  you,  is  there 
any,  and  if  so,  what  ?  To  include  real  dogs  among  mere 
possibilities  can  hardly  be  the  end  you  have  in  view.  You 
must  mean,  "  The  dogs  possess  this  attribute,  and  by  virtue  of 
this  attribute  are  related  to  other  possible  mammals."  The 
last  part  of  the  sentence  calls  for  interpretation.  "  Dogs,"  we 
must  read  it,  "  are  not  only  mammals  but,  supposing  anything 
else  to  be  mammal,  then  we  may  argue  a  relation  between  this 
thing  and  dogs."  What  relation  }  Surely  not  juxta-position  ; 
that  is  too  preposterous.  The  relation  meant  must  surely  rest 
on  nothing  whatever  but  the  joint  possession  of  the  attribute. 
The  inclusion  in  the  class  of  possible  mammals  means  nothing 
but  the  having  the  attribute  mammal,  and  in  addition,  a 
hypothetical  relation  of  identity  with  anything  else  of  the 
same  description.  We  predicate  two  things,  in  the  first  place 
a  quality,  and  then  a  relation  to  possible  objects  supposed  to 
have  the  same  quality.  Both  of  these  predicates  are  attributes, 
and  the  last  is  an  addition  which  may  be  superfluous.  It  is 
a  mistake  to  think  that  the  phrase  "  possible  "  will  help  us 
anywhere  into  anything  but  bad  metaphysics.  And  the 
favourite  prey  of  this  delusion  is  the  men  who  think  them- 
selves above  metaphysics.  1 r 

We  may  briefly  sum  up  this  matter  thus.  (The  only  way 
to  read  the  whole  judgment  in  extension  is  to  take  it  as  assert- 
ing a  relation  of  identity  between  different  individuals.  Two 
individuals  are  one  though  their  attributes  differ.  This  is 
simply  the  other  side  of  the  judgment  that  different  attributes 


1 68  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

are  interrelated  within  the  same  individual.  To  take  the 
subject  as  included  in  the  predicate  is  in  the  first  place  to 
substitute  fiction  for  fact,  and  in  the  next  place  is  to  predicate 
an  attribute  and  is  not  to  read  the  whole  judgment  in  ex- 
tension. But  if  the  subject  alone  be  taken  in  its  extension, 
then  what  is  asserted  is  obviously  a  connection  of  attributes 
within  an  individual  or  individuals. 


§  22.  Every  judgment  can  be  read  in  extension.  Although 
some  present  two  or  more  subjects  in  relation,  yet  all  can  be 
reduced  to  the  affirmation  of  a  connection  of  content  within 
one  subject.  In  "  A  is  to  the  right  of  B,"  the  whole  pre- 
sentation is  the  subject,  and  the  spatial  relation  of  A  to  Bis  an 
attribute  of  that.  In  "  Caesar  is  sick,"  the  same  person  is  said 
to  be  sick  as  well  as  Caesar.  And  in  "  Dogs  are  mammals," 
there  are  certain  things  which  are  declared  to  be  both.  In  this 
sense  of  extension  every  proposition  can  be  read  extensionally. 

We  have  now  to  ask  if  every  judgment  can  be  taken  in 
intension.  Can  not  only  the  predicate,  but  also  the  subject  be 
reduced  to  mere  content  t  Do  they  all  assert  a  connection  of 
attributes  ?  And  this  question  at  first  sight  may  be  answered 
in  the  negative.  In  "  Caesar  is  sick,"  we  certainly  have  a 
junction  of  adjectives,  but  it  will  be  said,  "  We  have  something 
else  beside.  Ther(p  is  the  individual  of  whom  these  qualities 
are  predicated  ;  and  this  individual  is  finite  and  determined. 
Admitted  that  in  every  intensional  judgment  you  have  a 
reference  to  the  ultimate  reality,  and  that  this  reality  is  indi- 
vidual, yet  the  ultimate  subject  does  not  affect  the  judgment. 
It  is  given  undetermined  except  so  far  as  it  is  determined  by 
the  judgment :  and  hence  it  does  not  interfere  with  the  con- 
nection of  the  adjectives.  But  when  you  have  a  finite  subject, 
then  that  subject  interferes.  In  *  Caesar  is  sick,'  the  judgment 
is  not  true  unless  you  make  it  of  this  one  Caesar.  You  can 
not  get  rid  of  the  individual  person,  and,  while  he  remains,  he 
prevents  your  reading  the  judgment  in  intension!' 

§  23.  We  have  already  cut  the  ground  from  under  this 
objection  by  proving  that  every  such  judgment  is  hypothetical 
and  strictly  universal  (Chap.  II.).  If  the  subject  is  taken  as  an 
existing  individual  or  set  of  individuals,  then  no  doubt  the  judg- 


Chap.  VI.]^  THE   QUANTITY   OF   JUDGMENTS.  169 

ment  is  categorical,  and  can  not  possibly  be  read  intensionally. 
"  All  these  six  sheep  have  got  the  rot,"  "  William  invaded  Eng- 
land," "  I  have  a  headache  :  "  if"  these  sheep,"  or  "  William,"  or 
"  I,"  are  taken  as  sensible  individuals  in  the  series  of  time,  then 
that  character  enters  into  the  assertion,  and  we  can  not  reduce  it 
to  a  hypothetical  synthesis  of  adjectives.  But  then  our  analysis  in 
Chapter  II.  has  shown  us  that  the  reduction  is  demanded.  When 
we  press  forthe  final  truth  of  the  judgment,  the  particular  subject 
becomes  an  unspecified  condition  of  the  content.  The  assertion 
is  thus  hypothetical.  It  conjoins  mere  adjectives,  though 
what  it  conjoins  is  vague  and  undetermined.  The  true  subject 
of  the  judgment  is,  not  this  or  that  finite  person  or  thing,  but 
the  ultimate  reality.  All  the  qualities  of  the  ostensible  subject 
pass  into  the  condition  of  a  universal  connection  of  attributes. 
It  would  be  idle  to  repeat  the  painful  enquiries  which  have 
established  this  result.  It  stands  or  falls  with  our  second 
chapter,  and  while  it  stands  it  carries  the  conclusion  that  every 
judgment  can  be  read  in  intension. 

§  24.  Thus,  when  the  ostensible  subject  is  a  particular 
phenomenon  or  collection  of  phenomena,  no  ordinary  means 
will  reduce  the  judgment.  To  take  it  in  intension  we  must 
apply  the  drastic  treatment  we  discussed  in  Chapter  II.  But 
in  other  instances  the  remedy  is  more  obvious,  and  is  easier  to 
administer.  "  Some  trespassers  must  be  prosecuted,"  "  Some 
English  citizens  are  to  be  hung,"  ''  In  some  impossible  cases 
right  would  be  wrong."  These  assertions  would,  I  presume, 
be  called  particular,  but  none  of  them  need  refer  to  this  or 
that  phenomenon.  The  "  some "  may  mean  "  under  some 
condition."  It  may  describe  the  attribute,  not  point  to  the 
individuals. 

There  are  cases  where  "  some ".  most  clearly  does  not 
indicate  this  or  that  particular  or  set  of  particulars.  "  Some 
crimes  are  deserving  of  capital  punishment,"  "  In  some  diseases 
the  patient  should  be  secluded  : "  we  mean  here  that,  given  a 
crime  or  disease  of  a  certain  sort  which  we  do  not  specify, 
then  something  else  would  in  that  case  follow.  The  judgment 
couples  mere  attributes  with  attributes.  It  does  not  assert  the 
existence  of  this  or  that  crime  or  disease.  It  is  hypothetical, 
and  is  naturally  read  at  once  in  intension. 


I/O  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

§  25.  "Some"  again  may  mean  an  unknown  number. 
"  Some  English  citizens  will  be  hung  next  year,"  may  mean, 
not  one  sort,  but  one  unspecified  quantity  of  English  citizens 
will  suffer  this  fate.  A  particular  event  is  here  asserted,  and 
the  proposition  must  in  the  end  be  reduced  by  the  method 
laid  down  in  Chapter  II.  But  the  event  it  foretells  has  already 
in  part  been  stripped  of  particularity.  The  forming  a  number, 
or  contributing  to  an  amount,  is  an  universal  attribute  :  it  is  a 
general  adjective,  and  to  this  extent  the  subject  has  been 
already  purified.  When  read  in  intension  the  judgment  runs 
thus,  "  Given  certain  conditions,  part  unspecified,  part  specified 
as  the  attribute  of  English  citizen  and  the  attribute  of 
amounting  to  a  certain  number,  then!'  etc. 

It  is  an  elementary  mistake  to  suppose  that  number  confers 
particularity  and  destroys  intension.  And  the  error  reveals 
a  deep  foundation  of  bad  metaphysics.  Number  is  surely 
nothing  but  an  attribute^  And  how  can  the  addition  of  an 
universal  quality  force  us  to  take  a  judgment  merely  in  ex- 
tension ?  How  can  it  even  help  towards  such  a  result }  You 
may  say,  perhaps,  that  nothing  is  numbered  save  actual 
phenomena,  but  such  an  assertion  would  be  incompatible  with 
fact.  "  In  the  single  case  of  two  men  being  three  men,  four 
men  would  be  six  men  " — this  is,  I  presume,  an  hypothetical 
judgment.  Not  only  can  you  take  it  as  connecting  attributes, 
but  I  do  not  see  how  you  can  take  it  otherwise.  It  is  idle  to 
object  that  the  subject  is  really  the  imagined  example,  where 
two  is  three,  and  that  this  example  is  a  particular  event.  For 
it  is  nothing  of  the  sort.  It  is  a  supposed  condition  which,  if 
it  existed,  would  really  be  single,  but  does  not  exist  and  will 
never  be  anything  real  at  all. 

§  26.  The  idea  that  a  numerical  subject  is  particular 
vanishes  as  soon  as  we  confront  it  with  facts.  The  numerical 
character  is  nothing  but  a  character.  It  is  nothing  but  an 
adjective,  and  no  adjective  or  accumulation  of  adjectives  will 
make  anything  else  than  an  abstract  universal^  Suppose 
that  a  phenomenon  is  capable  of  division  in  fact  or  in  idea. 
Its  divisibility  is  a  general  quality,  which  other  phenomena 
might  also  possess,  and  which  would  not  difference  one 
from   the   other.     To   be   regarded  as  a  collection   of  units 


Chap.  VL]  THE   QUANTITY   OF  JUDGMENTS.  I/I 

summed  by  means  of  addition  to  a  certain  quantity,  is  an 
attribute  not  special  to  any  single  phenomenon  :  it  can  in 
no  sense  bestow  uniqueness.  And  again,  if  the  subject  is 
taken  as  a  quantity  which  stands  in  a  certain  fractional  relation 
to  another  quantity,  it  is  absurd  to  think  that,  on  the  strength 
of  these  mere  qualities,  you  leave  universals  and  get  to  existence. 
"  If  a  penny  is  thrown  one  thousand  times,  half  the  number  of 
throws  will  most  probably  give  head  : "  we  have  here  a  purely 
intensional  judgment.  There  is  nothing  contained  in  it  but 
bare  universals  :  there  is  nothing  but  hypothetical  junctions  of 
adjectives.  Of  course,  if  you  say,  "  This  penny  in  half  its  throws 
will  now  give  heads,"  the  case  is  altered  :  but  the  numbers 
have  not  changed  it.  The  subject  is  particular,  not  because  it 
is  numerical,  but  because  it  is  not  so,  because  over  and  above 
it  has  now  been  taken  as  a  particular  fact.  It  must  be  reduced 
by  the  method  laid  down  in  Chapter  11.  But  so  far  as  it 
is  numerical  it  is  already  reduced,  and  is  already  nothing 
whatever  but  attributes. 

§  27.  We  may  pass  on  to  consider  another  superstition.  If 
the  intension  signifies  the  meaning  of  a  word,  and  the  ex- 
tension is  the  number  of  actual  objects  of  which  the  meaning 
can  be  truly  predicated,  then  both  extension  and  intension 
are  relative  to  our  knowledge,  and  naturally  fluctuate  with 
altering  experience.  For  instance,  "  mammal  "  is  a  term  whose 
meaning  has  changed  and  will  change.  We  can  fix  no  limit 
to  the  possible  information  the  word  may  convey,  for  we  do 
not  know  how  many  attributes  in  the  end  may  be  found  to 
be  implied  in  the  quality  of  giving  suck.  And  the  number  of 
objects  we  denominate  "  mammal  "  is  of  course  not  stationary. 
Such  considerations  may  seem  too  obvious  to  be  ignored,  but 
their  neglect  has  given  rise  to  a  serious  mistake. 

In  certain  judgments,  where  the  predicate  is  not  of  the 
"  essence  "  of  the  subject,  we  are  warned  that  an  intensional 
reading  is  impossible.  "  All  American  citizens  know  the  name 
of  their  President,"  is,  we  are  told,  to  be  taken  in  extension 
(Venn,  Symbolic  Logic,  p.  395).  It  can  not  connect  one  set  of 
attributes  with  another  set  of  attributes,  because  the  connection 
it  asserts  is  accidental.  But  the  mistake  here  is  obvious.  If 
I  know  every  single  American  citizen,  so  as  on  this  knowledge 


1/2  THE   PRINCIPLES   OF  LOGIC.  [Book  I. 

to  make  my  assertion,  I  surely  must  know  by  the  selfsame 
process  that  the  attribute  I  assert  exists  in  each.  After  I 
have  noticed  each  single  citizen,  it  is  one  of  his  attributes  and 
part  of  his  meaning  to  know  the  name  of  his  President,  and, 
before  I  have  done  so,  I  can  say  nothing  at  all.  If  the 
extension  is  increased,  so  also  is  the  meaning.  And  the 
objection  that,  if  the  mark  were  part  of  the  intension  of 
"  American,"  we  should  assert  it  of  American  citizens  in  the 
future  as  well  as  at  present,  may  at  once  be  dismissed.  If 
the  subject  stands  also  for  "  all  Americans  in  the  future,"  then 
the  attribute  becomes  at  once  part  of  their  meaning.  But,  if 
the  subject  is  confined  to  the  present  time,  then  the  mark  is 
the  meaning  of  "  present  Americans,"  and  you  have  no  right  to 
apply  it  beyond. 

The  judgment  is  particular,  not  in  the  least  because  it  is 
"  accidental,"  but  because  American  citizens  are  facts  in  time. 
It  would  be  just  as  particular  if  I  changed  it  into  "American 
citizens  are  Americans."  And  of  course  if  the  citizens  meant 
by  the  subject  are  neither  real  men,  nor  real  images,  but  mere 
possibilities,  the  judgment  is  hypothetical  at  once,  and  we 
need  not  have  recourse  to  Chapter  II.  to  effect  its  reduction. 

§  28.  This  same  mistake  lay  at  the  foundation  of  the 
doctrine  (§  4)  that  proper  names  have  no  "  connotation."  The 
meaning  is  not  fixed,  and  this  leads  to  the  idea  that  no 
meaning  exists.  The  simple  enquiry  "Is  the  denotation 
fixed  1 "  leads  at  once  to  the  result  that,  here  as  everywhere, 
intension  and  extension  fluctuate  together. 

Both  are  relative  to  our  knowledge.  And  the  perception 
of  this  truth  is  fatal  to  a  well-known  Kantian  distinction.  A 
judgment  is  not  fixed  as  "synthetic"  or  "analytic:"  its 
character  varies  with  the  knowledge  possessed  by  various 
persons,  and  at  different  times.  If  the  meaning  of  a  word  were 
confined  to  that  attribute  or  group  of  attributes  with  which  it 
set  out,  we  could  distinguish  those  judgments  which  assert 
within  the  whole  one  part  of  its  contents  from  those  which  add 
an  element  from  outside  (p.  132)  ;  and  the  distinction  thus 
made  would  remain  valid  for  ever.  But  in  actual  practice  the 
meaning  itself  is  enlarged  by  synthesis.  What  is  added  to-day 
is  implied   to-morrow.     We    may  even  say  that  a  synthetic 


Chap.  VI.]  THE   QUANTITY   OF  JUDGMENTS.  173 

judgment,  so  soon  as  it  is  made,  is  at  once  analytic.  Kant 
has  really  no  need  of  this  unfortunate  division,  which  he 
seems  to  have  inherited.  The  real  question  which  he  means 
to  ask  is.  What  kind  of  synthesis  does  each  judgment  contain, 
and  what  in  each  synthesis  is  the  principle  of  unity  ? 

§  29.  To  sum  up  the  result — a  proposition  is  read  inten- 
sionally,  when  both  subject  and  predicate  are  taken  as 
attributes  hypothetically  related.  Whenever  the  ostensible 
subject  is  no  individual  or  collection  of  individuals  the 
judgment  is  7iatiirally  understood  in  intension.  Where  the 
subject  is  one  or  more  actual  phenomena,  the  judgment  can 
not  be  interpreted  naturally  as  a  hypothetical  connection  of 
attributes.  But  although  not  natural,  this  interpretation  is 
legitimate,  and  is  also  necessary.  When  we  leave  first 
appearances  and  ask  for  truth,  we  find  that  any  phenomenal 
judgment,  whose  subject  refuses  to  be  taken  as  content,  is  a 
judgment  which  is  false  (Chapter  IL). 

The  error  we  must  avoid  is  the  idea  that  a  class  is  a 
mere  aggregate  of  individuals.  Such  aggregates  in  my  head 
or  outside  my  head  are  barren  mythology  :  they  do  not  really 
exist.  And  if  we  mean  by  a  class  a  possible  aggregate  of 
possible  *  individuals,  we  have  no  longer  any  collection.  For 
possibilities  occupy  no  place  in  the  series  of  events  connected 
with  perception.  They  are  not  actual  individuals,  but  merely 
ideal  A  possible  horse  is  anything  which  might  con- 
ceivably possess  the  qualities,  first  of  general  uniqueness,  and 
then  of  equine  nature  (Chap.  VII.).  Thus  if  the  class  means 
the  attribute  with  reference  to  a  hypothetical  collection,  to 
include  in  the  class  is  to  predicate  an  adjective.  It  is  to 
assert  an  attribute,  and  through  that  attribute  to  assert  a 
relation  of  identity  and  difference  with  any  other  instance. 

§  30.  We  have  by  this  time  had  perhaps  more  than  enough 
of  the  quantity  of  judgments,  and  yet  there  is  a  question 
we  have  not  fully  cleared  up.  The  distinctions  "universal," 
"  particular,"  and  "  singular,"  fall  under  quantity,  and  it  may 
be  well  that  we  should  more  definitely  state  here  the  meaning 
in  which  we  take  these  terms.  The  common  logic,  we  shall 
*  I  suppose  we  do  not  always  mean  '^judged  possible."     Cf.  p.  4  note. 


1/4  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

all  remember,  ranks  singular  and  universal  judgments  together, 
and  opposes  the  particular  to  both  of  these.  A  particular 
judgment  is  a  judgment  which  fails  to  take  the  subject  explicitly 
and  avowedly  in  the  whole  of  its  extension  ;  and  other  judg- 
ments are  considered  universal  because  in  them  you  have 
all  of  the  subject.  This  arrangement  we  shall  not  proceed  to 
discuss.  It  is  sufficient  for  the  technical  use  of  the  syllogism, 
and  it  is  perhaps  in  itself  not  so  foolish  as  it  seems  to  be. 
We  need  not  however  pause  to  examine  it.  We  may  be 
satisfied  if  we  succeed  in  making  clear  our  own  interpretation. 

§  31.  The  subject  is  not  only  beset  with  ambiguities,  but  it 
tends  at  each  moment  to  cross  the  border  and  to  enter  the 
field  of  metaphysics.  I  am  afraid  it  is  impossible  for  me  here 
to  defend  the  interpretation  which  I  have  adopted.  I  must 
content  myself  with  trying  to  exhibit  clearly  the  doctrine 
which  seems  metaphysically  true,  and  which  agrees  with  the 
logical  results  we  have  arrived  at. 

We  may  realize  some  difficulties  which  obscure  the  sub- 
ject, if  we  state  them  in  the  form  of  thesis  and  antithesis, 
(i)  Nothing  that  is  real  is  universal,  (ii)  All  that  is  real  is 
universal,  (iii)  Nothing  that  is  real  is  particular,  (iv)  Most 
that  is  real  is  particular.  I  believe  in  the  truth  of  all  these 
propositions,  and  will  endeavour  to  show  that  they  are  not  in 
conflict.     But  first  it  is  better  to  advocate  each. 

§  32.  (i)  Nothing  that  is  real  is  universal.  Indeed,  how 
should  it  be  ?  What  is  real  is  substantial  and  exists  by  itself : 
it  is  individual.  But  the  universal  is  nothing  whatever  but  an 
adjective.  It  is  an  epithet  divorced,  a  shadow  which  apart 
from  its  body  is  nothing,  and  can  not  exist. 

(ii)  Everything  that  is  real  is  universal.  How  can  it  be 
otherwise  }  For  what  exists  must  be  individual,  and  the 
individual  is  no  atom.  It  has  an  internal  diversity  of  content. 
It  has  a  change  of  appearance  in  time,  and  this  change  brings 
with  it  a  plurality  of  attributes.  But  amid  its  manyness  it 
still  remains  one.  It  is  the  identity  of  differences,  and 
therefore  universal. 

(iii)  And  so  we  see  that  No  real  is  particular.  For  if 
particular,  then  not  individual,  and  if  not  individual,  then 
non-existent.      The    particular    is    atomic.     It  excludes   all 


Chap.  VL]  THE   QUANTITY   OF  JUDGMENTS.  175 

difference.  It  is  itself  and  nothing  beyond  itself.  And  that 
self  is  simple  :  it  is  so  far  as  it  is  nothing  else.  The  true 
particular  in  respect  of  quality  is  shut  up  in  one  quality  ; 
relations  it  can  not  be  said  to  have ;  in  respect  of  time  it  has 
no  continuance,  and  in  space  it  can  not  occupy  extension.  Its 
existence  in  space  is  nothing  but  a  point,  in  other  words,  is 
nothing  spatial.  Such  a  particular  is  of  course  not  to  be 
verified  in  experience.  It  is  a  metaphysical  etis  rationis,  an 
abstract  universal  which  can  not  be  real. 

(iv)  And  it  can  not  be  real  because,  if  not  all,  at  least 
Most  reality  must  be  partiailar.  For  in  existence  the  indi- 
viduals which  are  real  are  finite.  To  some  extent  at  least 
they  are  defined  by  their  limits.  It  is  because  they  repel 
other  things  that  they  are  what  they  are.  Exclusion  by 
others,  and  exclusion  of  others,  enters  into  their  substance  ; 
and  where  this  is  there  is  particularity. 

§  33.  It  is  obvious  here  that  in  thesis  and  antithesis  words 
have  been  used  with  different  meanings.  And  this  result  we 
desired  to  establish.  The  abstract  universal  and  the  abstract 
•  particular  are  what  does  not  exist.  The  concrete  particular 
and  the  concrete  universal  both  have  reality,  and  they  are 
different  names  for  the  individual. 

What  is  real  is  the  individual  ;  and  this  individual,  though 
one  and  the  same,  has  internal  differences.  You  may  hence 
regard  it  in  two  opposite  ways.  So  far  as  it  is  one  against 
other  individuals,  it  is  particular.  So  far  as  it  is  the  same 
throughout  its  diversity,  it  is  universal.  They  are  two  dis- 
tinctions we  make  within  it.  It  has  two  characters,  or  aspects, 
or  sides,  or  moments.  And  you  consider  it  from  whichever 
side  you  please,  or  from  the  side  which  happens  for  the  purpose 
of  the  context  to  be  the  emphatic  or  essential  side.  Thus  a  man 
is  particular  by  virtue  of  his  limiting  and  exclusive  relations  to 
other  phenomena.  He  is  universal  because  he  is  one  through- 
out all  his  different  attributes.  You  may  call  him  particular,  or 
again  universal,  because,  being  individual,  he  actually  is  both, 
and  you  wish  to  emphasize  one  aspect  or  side  of  his  indivi- 
duality. The  individual  is  both  a  concrete  particular  and  a 
concrete  universal  ;  and,  as  names  of  the  whole  from  different 
points  of  view,  these  both  are  names  of  real  existence. 


1/6  THE   PRINCIPLES  OF  LOGIC.  [Book  L 

§  34.  The  abstract  universal  and  abstract  particular  are 
both  unreal,  because  neither  are  names  for  the  individual. 
They  take  the  two  aspects  or  characters  of  the  whole,  and, 
turning  them  into  independent  existences,  then  assert  their 
reality.  But  one  side  of  a  whole  can  not  stand  by  itself 
except  in  our  heads.  It  is  nothing  but  an  adjective,  an 
internal  distinction  which  we  try  to  take  as  substantial  fact. 
We  can  all  see  that  this  holds  good  of  abstract  universals.  The 
oneness  or  identity  of  a  man,  we  know,  is  not  found  when  we 
search  the  series  of  mental  phenomena.  But  the  same  is  true 
of  the  abstract  particular.  If  you  take  atoms  seriously,  and 
deny  their  extension,  you  find  at  once  you  are  dealing  with 
something  which  can  not  be  fact.  Mere  exclusion  in  space  of 
other  spaces  is  nothing  real.  A  reality  in  space  must  have 
spatial  diversity,  internal  to  itself,  and  which  it  does  not 
exclude.  And  this  holds  again  with  psychical  atoms.  For, 
as  observed,  they  have  internal  multiplicity,  duration  in  time, 
quality,  and  degree  ;  and  as  anything  else  they  could  not  be 
observed.  An  atom  which  really  was  particular,  which  was 
not  divisible  at  least  in  idea,  could  not  possibly  be  fact.  It  is 
one  aspect  of  fact  torn  away  from  the  rest,  and  is  nothing  in 
itself  and  apart  from  the  act  which  tears  it  away. 

§  35.  The  abstract  particular  and  the  abstract  universal 
are  mental  creations,  which,  if  taken  as  fact  outside  our 
heads,  are  different  examples  of  the  same  mistake.  Both  are 
distinctions  within  a  whole,  hardened  into  units  that  stand  by 
themselves.  And  not  only  do  they  spring  from  the  same 
mistake,  but  we  may  even  say  that  they  are  the  same  error. 
The  abstract  triangle  in  and  by  itself  is  found  to  exclude  all 
further  predicates  (cf.  p.  1 14).  Determined  by  that  division 
and  consequent  exclusion  which  gave  it  its  origin,  it  has 
become  particular.  And  the  particular  itself,  because  produced 
by  mental  separation,  is  really  no  more  than  an  adjective 
divorced,  or  abstract  universal.  The  dialectical  method  has 
laboured  to  show  that,  here  as  everywhere,  insistance  upon  a 
onesided  view  brings  out  by  negation  the  opposite  onesidedness. 
The  universal,  the  more  we  emphasize  its  character,  divides 
itself  the  more  from  the  whole.  We  make  its  being  depend 
on  exclusion,  and  it  turns  in  our  hand  into  its  logical  contrary. 


Chap.  VI.]  THE   QUANTITY   OF  JUDGMENTS.  .         1 7/ 

The  particular  again,  excluding  others,  and  being  so  far  as  it 
merely  excludes,  is  its  own  negative  relation  to  other  particulars. 
It  falls  beyond  itself  into  a  series  of  units  pervaded  by  an 
universal  identity,  and  itself  has  there  become  its  own  opposite. 
In  this  speculative  movement,  if  we  take  it  in  the  character  it 
claims  for  itself,  I  neither  myself  profess  belief  nor  ask  it  from 
the  reader.  But  I  think  we  may  go  so  far  as  this,  that  in  the 
end  the  individual  is  real,  and  that  abstract  universal  and 
abstract  particular  are  distinctions  taken  within  that  reality, 
which  a  mistake  has  afterwards  turned  into  divisions  and 
hardened  into  units.  If  we  do  not  admit  that  each  is  a 
moment  which,  by  negation  of  itself,  affirms  the  other  and 
begets  the  whole,  we  may  certainly  say  that  each  has  sprung 
from  the  same  mistake,  and  is  an  illusion  of  the  self-same  kind. 
And  we  may  muster  courage,  perhaps,  to  profess  that  the 
individual  is  the  identity  of  universal  and  particular. 

§  36.  We  must  keep  in  view  the  following  distinctions. 
We  have  first  the  abstract  universal  and  particular,  and  neither 
of  these  can  exist  in  nature.  On  the  other  side  we  have  the 
individual,  and  the  individual  is  the  only  thing  which  is  real. 
But  where  this  real  is  finite -it  may  be  taken  from  two  points 
of  view  :  it  is  concrete  particular  or  concrete  universal.  In  so 
far  as  it  is  a  finite  individual  which  excludes  all  others,  so  far 
it  is  a  relative  particular.  But  because  it  includes  a  diversity 
of  content,  it  is  therefore  also  a  relative  universal. 

There  is  here,  I  confess,  a  doubtful  point  I  am  forced  to 
leave  doubtful.  It  might  be  urged  that,  if  you  press  the 
enquiry,  you  will  be  left  alone  with  but  a  single  individual. 
An  individual  which  is  finite  or  relative  turns  out  in  the  end 
to  be  no  individual  ;  individual  and  infinite  are  inseparable 
characters.  Or  again,  it  might  be  said,  the  individual  is  finite, 
and  there  can  not  be  an  absolute  individual.  Metaphysics,  it 
is  clear,  would  have  to  take  up  these  questions,  and  in  any 
case  to  revise  the  account  which  is  given  in  this  chapter.  But 
that  revision  must  be  left  to  metaphysics  ;  and  for  the  purposes 
of  logic  we  may  keep  the  distinctions  already  laid  down.  We 
have  (i)  the  real,  supposed  to  fall  into  {a)  absolute  individual 
or  concrete  universal,  (b)  relative  individual  or  concrete  uni- 
versal or  concrete  particular ;  and  (ii)  the  unreal,  consisting 

N 


178  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

{a)  of  the  abstract  universal,  and  {b)  of  the  abstract  or  absolute 
particular. 

§  37.  We  may  now  attempt  to  lay  down  what  we  mean  by 
2mwersal  judgments.  .  Such  a  judgment  is  one  whose  subject 
is  universal.  And  it  is  obvious  that  here  we  have  more  than 
one  meaning.  An  universal  judgment  may  be  (i)  absolute, 
or  (ii)  relative. 

(i)  In  the  first  case  we  have  again  two  divisions.  Such  a 
judgment  may  {a)  be  abstract,  or  again  (d)  may  be  concrete. 
If  (a)  the  judgment  is  abstract,  the  ostensible  subject  will  of 
course  be  an  attribute.  The  statement  will  truly  be  hypo- 
thetical, since  the  actual  subject  is  non-phenomenal  reality. 
The  ordinary  kind  of  universal  judgment  such  as  "The  angles 
of  a  triangle  are  equal  to  two  right  angles  "  is,  as  we  have  seen 
(Chap.  II.),  of  this  description.  And  it  is  universal  for  two 
reasons.  The  grammatical  subject  is  an  abstract  universal  : 
while  the  actual  subject,  the  ultimate  reality,  is  a  concrete  uni- 
versal and  is  also  absolute.  This  is  the  first  and  more  ordinary 
kind  of  judgment  which  we  are  able  to  call  absolutely  universal. 
But  (^)  it  is  necessary  to  mention  another  sort.  Any  state- 
ment made  concerning  a  reality  which  is  not  considered  finite 
will  also  be  an  absolute  universal  judgment.  Nothing  will  fall 
outside  the  subject,  and  the  predication  will  be  categorical.  I 
do  not  say  that  such  judgments  are  practicable ;  but  they  are 
logically  possible,  and  must  be  provided  for. 

§  38.  (ii)  A  judgment  is  relatively  universal  where  the 
subject  is  a  finite  individual  or  collection  of  individuals.  It  is 
universal,  because  the  subject  is  the  identity  of  its  own  internal 
diversity.  In  "  Caesar  is  sick,"  Caesar  is  not  affirmed  to  be 
nothing  but  sick  :  he  is  a  common  bond  of  many  attributes, 
and  is  therefore  universal.  But  this  judgment  is  relative, 
because  Caesar  is  one  man  among  other  men  ;  and,  if  you  take 
him  so,  he  himself  is  particular. 

§  39.  (A  judgment  which  is  absolutely  particular  can  not 
exist.  It  would  have  a  subject  completely  shut  up  and  con- 
fined in  the  predicate.  And  such  a  judgment,  if  it  came 
into  being,  would  not  be  a  judgment.  For  it  obviously  would 
say  nothing  else  of  the  subject  or  predicate  than  themselves. 
"  This  is  this  "  may  be  taken  as  the  nearest  example,    j 


Chap.  VI.]  THE   QUANTITY    OF   JUDGMENTS.  179 

A  relative  particular  judgment  is  one  where  the  subject 
is  this  or  that  singular  or  collection.  It  is  the  same  as  the 
relative  universal  judgment,  but  is  taken  from  another  side  of 
its  nature.  The  subject  excludes  all  other  individuals,  and  so 
is  particular  ;  but  within  itself  it  has  a  diversity,  and  so  is 
universal.  It  possesses  attributes  other  than  the  predicate, 
and  may  be  taken  within  another  context.  It  thus  serves  as 
a  middle  term  in  reasoning,  as  is  shown  in  the  third  of  the 
syllogistic  figures. 

§  40.  We  have  seen  before  (Chap.  II.  §  45)  that  no 
logical  difference  separates  the  singular  and  collective  judg- 
ments. It  is  ridiculous  to  think  that  if  one  individual  is  not 
universal,  you  reach  universality  by  adding  on  others.  The 
number  of  units  is  quite  irrelevant,  since,  however  many  they 
become,  each  remains  a  singular.  And  this  or  that  collection 
of  individuals  is  as  hard  a  particular  as  any  individual  found 
in  the  collection.  Nay,  from  this  point  of  view,  the  single 
individual  himself  turns  out  to  be  a  mere  collection.  Con- 
sidered logically  they  are  both  alike.  Excluding  others,  they 
are  relative  particulars.  Common  to  all  their  internal  diversity 
and  identical  throughout  it,  they  both  alike  are  relative 
universals. 

§  41.  No  judgment  has  or  can  have  a  subject  shut  up 
within  the  limits  of  one  single  predicate.  If  we  remain  at  the 
popular  point  of  view,  and  admit  those  judgments  where  the 
subject  is  nothing  but  a  finite  phenomenon  or  set  of  phenomena, 
yet  even  these  judgments  are  universal  relatively.  The  subject 
will  serve  as  a  middle  in  reasoning.  It  is  hence  the  identity  of 
differences,  and  it  could  not  be  that  if  it  were  only  particular. 
Every  judgment  is  thus  universal,  and  in  the  end  they  all  may 
be  said  to  be  universal  absolutely.  For,  if  we  exclude  the 
possibility  of  non-phenomenal  finite  individuals,  we  have  shown 
(Chap.  II.)  that  every  judgment  to  be  true  must  predicate  of 
the  absolute  individual,  either  hypothetically  or  categorically. 
And  the  former  of  these  cases  must,  in  the  end,  be  reduced  to 
the  latter.  The  finite  subject  changes  in  our  hands  into  a  heap 
of  mere  adjectival  conditions,  and,  since  these  conditions  can 
never  be  complete,  the  statement  loses  its  categorical  force. 
But  becoming   hypothetical  it  predicates  indirectly  a  latent 

N  2 


l80  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

quality  of  the  ultimate  reality,  and  so  once  more  is  categorical, 
true  categorically  of  the  absolute  subject. 

§  42.  All  judgments  are  thus  alike  universal,  but  it  can 
not  be  said  they  are  universal  equally.  If  the  subject  of  one 
judgment  is  a  whole  which  includes  the  subject  of  another,  the 
first  is  certainly  the  more  universal.  And  again,  if  we  take 
two  abstract  judgments,  they  are  both  hypothetical,  but  the 
one  may  assert  a  more  abstract  connection  than  is  affirmed  in 
the  other.  The  purer  hypothesis,  the  one  most  set  free  from 
irrelevant  conditions,  will  be  also  more  true.  It  will  predicate 
in  a  higher  sense  of  the  universal  subject,  and  therefore  may 
be  called  the  more  universal.  But  if  the  connection,  although 
less  concrete,  is  not  more  pure,  we  must  then  not  call  one 
judgment  more  universal  than  the  other,  unless  we  qualify 
universal  by  abstract. 

§  43.  I  will  repeat  in  conclusion  the  distinctions  it  is  right- 
we  should  keep  in  mind.  The  real  is  individual.  The  merely 
universal  or  merely  particular  are  unreal  abstractions.  Con- 
crete universal  and  concrete  particular  are  the  individual  from 
different  points  of  view.  But  we  could  not  say  that  an  absolute 
individual  was  really  particular,  since  it  would  have  no  relation 
to  anything  outside. 

.Particular  judgments,  if  taken  categorically,  are  precisely 
the  same  as  relative  universal.  The  phenomenal  individual, 
or  collection  of  individuals,  is  the  identity  of  diverse  relations 
and  qualities.  Universal  judgments  are  relative  or  absolute. 
If  relative,  they  are  the  same  as  particular  judgments.  If 
absolute,  they  are  either  hypothetical  or  categorical.  In  the 
first  the  ostensible  subject  is  an  abstraction  :  in  the  second  it 
must  be  the  ultimate  reality.  Particular  categorical  judgments 
may  all  be  reduced  to  abstract  or  hypothetical  universals,  and 
these  again  to  categorical  universals.  In  the  end  all  truth,  if 
really  true,  is  true  of  the  ultimate  non-phenomenal  fact. 


(     I8i     ) 


CHAPTER  VII. 

THE   MODALITY   OF  JUDGMENTS.* 

§  I.  Modality  is  not  an  alluring  theme.  I  should  be  glad 
to  plead  the  fragmentary  nature  of  the  present  work  as  an 
excuse  for  passing  it  by  in  silence.  But  for  the  sake  of 
clearness  it  is  necessary  to  make  an  excursion  into  the  subject, 
neglecting  those  parts  of  it  which  do  not  seem  to  concern  us 
here. 

We  must  begin  by  stating  an  erroneous  view.  Modality 
may  be  supposed  to  affect  the  assertion  in  its  formal  character, 
and  without  regard  to  that  which  is  asserted.  We  may  take 
for  instance  a  content  S  —  P,  not  yet  asserted,  and  may  claim 
for  modality  the  power  of  affirming  this  content  S  —  P, 
unaltered  and  unqualified,  in  several  ways.  S  —  P,  it  is 
supposed,  may  be  asserted,  for  instance  either  simply  or 
problematically  or  apodeiktically,  and  may  yet  remain 
throughout  S  —  P  :  and  thus,  though  the  content  is  unmodified, 
the  assertion  is  modal. 

§  2.  This  doctrine  rests  on  a  misunderstanding.  There 
are  no  degrees. of. Jtruth  and  falsehood.  If  S  —  P  is  fact,  it 
can  not  be  more  than  fact  :  if  it  is  less  than  fact,  it  is  nothing 
at  all.  The  dilemma  is  simple.  S  —  P  is  affirmed  or  it  is  not 
affirmed.  If  it  is  not  affirmed,  it  is  not  judged  true  at  all.  If 
it  is  affirmed,  it  is  declared  to  be  fact,  and  it  can  not  be  more 
or  less  of  a  fact.  There  clearly^  can  be  but  one  kind  of  judg- 
ment, the  assertorical.  Modality  affects  not  the  affirmation, 
but  what  is  affirmed.  It  is  not  mere  S  —  P  that  is  asserted 
modally :  it  is  another  content,  a  modified  S  —  P.  In  other 
words,  you  do  not  say  that  the  mere  idea  S  —  P  holds  good 

*  Cf.  Sigwart,  Logik,  pp.  189  and  following. 


182  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

in  fact :   you  first  say  something  else  about  S  -  P,  and  it  is 

then  this  new  and  different  idea  which  really  is  asserted. 

i       §  3.  Modality  in  this  sense,  it  has  been  rightly  observed, 

''hasv^io  natural  limits.  There  are  endless  ways  of  modifying  a 
judgment  so  as  to  make  a  fresh  judgment.  You  may  take 
the  idea  of  a  judgment  S  —  P  and  express  any  attitude  of 
your  mind  towards  it.  You  may  say  "  I  make  it,"  or  "  wish  to 
make  it,"  or  "  fear  to  make  it,"  or  "  can  not  make  it,"  or  "  am 
inclined  to  make  it,"  or  "  am  forced  to  make  it."  All  these  are 
simple  assertorical  statements  about  my  condition  of  mind. 

^They  have  a  psychological  not  a  logical  bearing,  and  may  at 
once  be  dismissed.'' 

§  4.  The  different  ways  in  which  we  can  stand  to  a  judg- 
ment S  —  P  are  a  matter  for  psychology  rather  than  for  logic. 

y'Logical  modality  must  be  limited  to  that  which  seems  to  affect 
the  idea  S  —  P,  and  to  affect  it  in  its  relation  to  the  world  of 
reality.  If  we  say,  "  I  wish  S  —  P  were  a  fact,"  this  once 
more  is  a  psychological  mode.  The  content  S  —  P  is  not 
here  first  modified  and  then  attributed  to  the  ultimate  subject. 
Neither  itself  nor  anything  we  can  call  a  modification  of  itself, 
pretends  to  be  either  true  or  false.  The  judgment  in  fact  is 
concerned  with  nothing  but  my  mental  attitude. 

Either  logic  has  nothing  to  do  with  modality,  or  modality 
affects  S  —  P  from  the  side  of  truth  and  falsehood.  The  ideal 
content  must  be  referred  to  or  else  denied  of  reality.  But  the 
reference  or  the  denial  itself  is  simple,  and  can  not  be  modified. 
What  therefore  must  in  some  way  be  modified  is  the  content 
itself  Not  S  —  P  but  a  transformed  and  conditioned  S  ~  P 
is  the  assertion  made  by  logical  modality. 

.  §  5.  The  modes  of  S  —  P  which  logic  has  to  consider  are 

\  three  in  number.  In  each  case  we  assert,  we  refer  some  idea 
to  ultimate  fact,  we  begin  the  judgment  by  saying,  "  It  is  true," 
— but  we  go  on  to  fill  up  the  blank  in  each  case^by  a  different 
idea.  It  is  true  that  S  —  P  is  actual,  or  is  ff^sible,  or  again 
is  Necessary.  The  idea  pronounced  true  is  "  actual  S  —  P,"  or 
"  possible  S  -  P,"  or  "  necessary  S  -  P."  These  modes  we 
retain  for  consideration,  dismissing  all  others.  But  our  choice 
is  'iiot  really  so  arbitrary  as  it  seems.  We  have  here  in  a 
veiled  andvhidden  shape  the  distinction  of  categorical  and 


Chap.  VII.]  THE   MODALITY   OF  JUDGMENTS.  1 83 

hypothetical  assertion.  The  possible  and  the  necessary  are 
special  forms  of  the  hypothetical ;  and  between  the  assertorical 
and  the  categorical  there  is  no  difference  whatever. 

I  shall  begin  by  asking  (i)  the  general  meaning  which  in 
logic  we  assign  to  the  predicates  possible,  necessary,  and  real. 
I  shall  then  point  out  (ii)  that  the  possible  and  the  necessar}^ 
have  lib  real  existence.  But  on  the  other  hand  I  shall  show 
(iii)  that  these  modal  assertions,  though  as  such  and  in  them- 
selves they  are  not  true  of  fact,  must  always  rest  on  a  basis  of 
assertion  which  is  true  or  false  of  actual  reality. 

§  6.  (i)    We  need  not  ask  what  we  mean  by  (a)  asser- 
torical judgment.    It  is  judgment  categorical  or  unconditioned,  t^ 
"  S  —  P  is  real,"  attributes  S  —  P,  directly  or  indirectly,  to  the 
ultimate  reality.      And  on  this  point  we  have  nothing  to  add 
to  the  explanations  already  given  in  Chapter  II.      The  asser- 
torical judgment   may  be  dismissed  from  our  thoughts.     Tc 
draw  a  difference  between  a  categorical  judgment  on  the  on^  ' 
hand,  and  on  the  other  a  judgment  which  asserts  reality,  \i  ^^^ 
plainly  impossible.     The  assertorical  is  simply  the  categorical; 
taken  in  contrast  with  the  possible  and  the  necessary. 

§  7.  And  these  are  nothing  but  phases  of  the  hypothetical. . 
What   may   be    and    what   must    be   involve   a  supposition. 
Neither  is  declared  to  be  actual  fact :    they  both  are  inferred 
on  the  strength  of  a  condition,  and  subject  to  a  condition. 

{]))  It  is  easy  to  give  the  general  sense  in  which  we  use  the 
term  necessity.  A  thing  is  necessary  if  it  is  taken  not  simply 
in  and  by  itself,  but  by  virtue  of  something  else  and  because 
of  something  else.  (Necessity  carries  with  it  the  idea  of 
mediation,  of  dependency,  of  inadequacy  to  maintain  an  " 
isolated  position  and  to  stand  and  act  alone  and  self-supported. 
A  thing  is  not  necessary  when  it  simply  is ;  it  is  necessary 
when  it  is,  or  is  said  to  be,  because  of  something  else.      ) 

And  where  necessity  is  "  internal,"  this  meaning  is  retained. 
For  it  is  not  the  totality  which  in  this  case  is  necessitated. 
There  is  a  diversity  of  elements  contained  in  the  whole,  and 
these  elements  are  divided  into  that  which  constrains  and  that 
which  follows.  In  an  unseparated  world  there  could  be  no 
necessity. 

§  8.  In  a  work  on  metaphysics  the  word  "  because  "  would 


1 84  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

lead  us  straight  to  some  fundamental  difficulties,  which  will 
meet  us  again  in  our  concluding  Book.  Is  there  any  because 
outside  of  our  heads  ?  Is  it  true  that  one  thing  is  by  means 
of  another,  and  because  of  another  ?  Or  are  we  forced  to 
admit  that  every  fact,  while  it  is  no  doubt  and  is  also  perhaps 
together  with  others,  is  not  an  adjective  depending  on  these 
others,  has  no  real  bond  that  fastens  it  to  its  environment, 
nor  is  subject  to  any  alien  influence  ?  The  objection  would 
assail  us  :  " '  One  fact  is  and  another  fact  is,'  so  much  is  true  ; 
but  *  One  fact  is  and  so  another  fact  is,'  must  always  be  false. 
It  is  giving  reality  to  mere  ideal  connections."  And,  if  we 
escaped  this  objection,  we  should  find  another  lying  in  wait  for 
us.  "  You  may  say  that  one  reality  is  the  cause  of  another, 
and  you  may,  if  you  please,  add  to  this  that  the  second  is 
because  of  the  first.  But,  if  you  venture  to  convert  this 
assertion,  and  assume  that  whenever  you  have  a  because  you 
have  also  a  cause,  you  fall  into  error  of  the  worst  description. 
VA  cause  is  real,  a  because  is  ideal ;  you  may  have  the  one  and 
do  often  have  it,  where  the  other  is  impossible.  They  do  not 
always  co-exist ;  and  where  they  do  co-exist,  they  do  not 
always  coincide ;  and  where  they  coincide,  they  are  not 
identical.  They  are  not  the  same  thing  :  they  are  not  even 
two  different  faces  of  the  same  thing.  They  are  nothing  but 
counterparts,  two  parallel  series  which  have  no  common  points 
but  possess  some  terms  which  have  a  constant  relation " 
(Book  III.). 

§  9.  In  a  work  of  this  kind  we  can  not  grapple  with  the 
problems  offered  us.  We  must  here  admit  the  objection  and 
retire  before  it.  We  must  admit  that  in  logic  "  because  "  does 
not  stand  for  a  real  connection  in  actual  fact :  we  must!/ 
allow  that  necessity  is  not  a  bond  between  existing  things.* 
For  logic  what  is  necessary  is  nothing  beyond  a  logical 
consequence.  Necessity  is  here  the  force  which  compels 
us  to  go  to  a  conclusion,  if  we  start  from  premises.  The 
*  because "  expresses  an  ideal  process  of  mental  experiment, 
which  gives  as  its  result  a  certain  judgment.  It  does  not 
guarantee  the  truth  of  this  judgment,  if  you  take  it  by  itself 
It  does  not  guarantee  the  truth  of  the  data  which  the  process 
starts  from,  and   on   which  it  operates.     A  necessary  truth 


Chap.  VII.]  THE   MODALITY  OF  JUDGMENTS.  1 85 

may  be,  and  commonly  is,  categorical,  but,  so  far  as  its 
necessity  goes,  it  is  hypothetical.  It  ceases  to  be  hypothetical 
only  when  it  ceases  to  be  merely  necessary. 

§  10.  I  admit  it  is  not  the  same  thing  to  affirm  "//"  M  is 
P  then  S  is  P,"  and  "  Since  M  is  P  therefore  S  is  P."  And  the 
difference  is  obvious.  In  the  latter  case  the  antecedent  is 
a  fact,  and  the  consequent  is  a  fact :  they  are  both  categorical 
(Chap.  II.  §  71).  In  the  former  case  the  antecedent  may  be 
false  and  the  consequent  impossible.  But  the  necessity  in 
each  case  is  one  and  the  same.  >  S  —  P  mnst  be  true,  if  you 
take  M  —  P,  and  take  S  -  M,  and  draw  the  conclusion.  That 
is  all  the  necessity  it  is  possible  to  find.  The  knowledge 
that  S  -  M  M  -  P  are  both  true,  and  that  S  -  P  is  a  statement 
which  holds  of  fact,  falls  outside  the  necessity  and  does  not 
increase  it.  The  hypothetical  result  becomes  categorical  by 
an  implied  addition.  And  the  hypothetical  connection  may 
not  even  then  become  categorical,  [^he  bond  of  necessity  is  a 
logical  passage,  and  to  say  that  this  logical  passage  itself  exists 
in  fact  demands  an  assumption  which  can  not  be  hazarded 
in  the  face  of  objection^  In  logic  we  must  be  content  to  say 
that,  if  the  premises  are  categorical,  the  result  is  categorical. 
We  can  not  add  that  this  result  is  necessary,  unless  for  a 
moment  we  treat  the  data  as  hypotheses,  and  mean  no  more 
than  7/  S  -  M  M  -  P  are  given,  then  S  -  P  must /^//^w. 

§  II.  We  are  able  to  urge  a  two-fold  argument  to  show 
that  necessity  is  hypothetical.  We  can  reason  from  principle, 
and  again  from  usage.  The  argument  from  principle  we  may 
repeat  as  follows.  Logical  necessity  is  an  ideal  process,  and 
you  can  not  assume  that  either  ideas  or  process  are  facts. 
Even  if  the  ideas  exist  in  fact,  and  exist  in  corresponding 
sequence,  you  can  not  assume  that  in  this  sequence  your 
process  exists.  Your  ideal  operation  works  with  ideas,  and, 
so  far  as  you  know,  it  works  only  with  ideas.  The  idea  may 
be  more  than  a  mere  idea,  but  it  is  as  an  idea  that  it  goes 
into  the  experiment.  And  a  mere  idea  is  no  more  than  a 
mere  supposal.  The  result,  so  far  as  necessitated,  is  there- 
fore so  far  7iot  categorical.  This  we  may  call  the  argument 
a  priori. 

And  we  have  in  addition  an  argument  from  usage.     A 


1 86  THE  PRINCIPLES   OF  LOGIC.  [Book  1. 

necessary  judgment,  a  statement  introduced  with  "  It  must  be 
so,"  may  assert  what  not  only  fails  to  be  actual  but  is  plainly^ 
impossible.  "  If  two  were  three  then  four  must  be  six " 
presents  us  with  a  truth  which  is  compulsory.  The  result  must 
follow  ;  it  is  necessary  truth  ;  but  it  does  not  follow  in  actual 
existence,  and  could  not  follow  there,  since  both  antecedent 
and  consequence,  and  their  actual  junction,  are  impossibilities. 
It  is  not  true  that  apodeiktic  modality  strengthens  our"^ 
assertions.  It  serves  rather  to  weaken  them.  If  S  is  P,  there 
is  an  end  of  doubt.  If  S  must  be  P,  we  know  indeed  that, 
given  something  else,  we  can  be  sure  of  S  ~  P,  but  we  are 
certain  of  no  more.  The  apodeiktic  mode  either  leaves  our 
doubts,  or  removes  them  only  by  the  covert  assertion  of  the 
condition  of  S  — P.  Where  the  necessary  asserts  strongly 
it  borrows  its  strength  from  a  concealed  assertorical.  I 
will  conclude  this  section  in  Sigwart's  words.  "There  is  a 
common  idea  that  the  apodeiktic  judgment  stands  for  some- 
thing higher  than  the  assertorical.  It  is  believed  that,  if  we 
start  from  the  problematic  judgment  and  ascend  to  the  apo- 
deiktic, we  steadily  increase  the  certainty  of  our  knowledge, 
and  add  to  the  worth  and  dignity  of  our  assertions.  This 
idea  must  be  relinquished.  All  mediate  certainty  must  stand 
in  the  end  on  immediate  knowledge  :  the  ultimate  premises  of 
every  proof  can  not  be  proved.  The  usages  of  life  stand  in 
comic  discrepancy  with  the  emphasis  we  lay  upon  apodeiktic 
certainty.  The  sayings  *It  must  be  so,'  'It  must  have  so 
happened,'  are  judgments  apodeiktic  :  but  the  confidence  they 
express  has  most  modest  limits."     {Logik,  I.  195.) 

§  12.  {c)  A  necessary  truth  is  a  truth  which  results  from 
assumed  conditions.  If  we  imply,  as  we  very  commonly  do, 
that  those  conditions  are  actual,  then  the  result  is  categorical. 
But,  though  the  necessary  may  be  real,  its  necessity  is  hypo- 
thetical. What  have  we  now  to  say  about  possibility  ?  When 
S  — P  is  possible,  does  that  mean  that  S  — P  would  exist  as 
fact,  if  something  else  were  fact  ^  Is  possibility  in  short  a 
form  of  hypothetical  necessity  ? 

It  sounds  strange  when  we  hear  that  the  possible  falls 
under  the  head  of  the  necessary.  But  it  is  at  least  as  sur- 
prising  to  learn    that  the    necessary  may    be  impossible  or 


Chap.  VII.]  THE   MODALITY   OF  JUDGMENTS.  1 8/ 

non-existent ;  and  this  we  already  -know  to  be  the  case. 
On  such  subjects  as  these  our  first  impressions  may  be  worth 
very  Httle. 

The  possible  is  that  which  is  known  or  assumed  to  be  the 
consequence  of  certain  conditions.  So  far  the  possible  is 
one  with  the  necessary,  where  it  is  implied  that  the  antecedent 
is  real.  But  it  differs  in  this  point ;  for  S  —  P  to  be  possible 
all  the  conditions  which  make  S  —  P  necessary  must  be  sup- 
posed, but  only  a  part  of  them  need  be  assumed  to  exist.  It 
is  implied  that  a  part  of  the  antecedent  exists,  but  as  to  the 
other  part  we  are  left  in  ignorance.  Thus  ih^  partial  existence 
of  the  conditions  of  S  —  P  is  the  differentia  which  separates 
the  species  "  possible "  from  the  genus  "  necessary."  Take 
a  judgment  such  as  this,  Given  abed  then  E  must  follow. 
Add  to  it  the  judgment,  or  the  supposition  (§  15),  that  ab 
exists,  while  cd  is  not  known  to  exist,  and  we  get  the  possible. 
E  is  now  a  possibility.  We  have  an  assumed  fact  ab,  we  also 
have  ideal  conditions  c  and  d,  assumed  to  be  compatible  with 
ab,  but  not  taken  to  exist.  We  have  a  hypothetical  judg- 
ment, Given  abed,  we  should  have  E.  And  from  this,  by 
the  assumption  that  ab  exists,  we  pass  to  "  We  may  in  fact 
have  E."  In  other  words  ab  is  the  "  real  possibility  "  of  the 
possible  E.  It  is  known  to  be  real,  or  at  least  is  treated  as  if 
it  were  so  known  (§  15). 

§  13.  Everything  possible  must  be  really  possible.  It 
must  stand  on  a  reality  assumed  to  exist,  and  taken  as  part  of 
that  sum  of  conditions  which  would  make  S  —  P  an  actual 
fact.  Possibility  apart  from  or  antecedent  to  the  real  world  is 
utter  nonsense. 

But  the  basis  of  fact  may  vary  indefinitely.  S  — P  is 
possible  in  the  highest  sense  when  the  detailed  conditions 
which  make  it  necessary  are  fully  known,  and  a  part  of  these 
detailed  conditions  is  also  taken  to  exist.  This  highest  sense 
sinks  by  slow  degrees  to  the  lowest  of  all,  where  "  possible  " 
stands  for  "  not  known  to  be  impossible."  Here  we  do  not  know 
what  special  conditions  give  S  —  P.  Our  basis  of  fact  is  nothing 
but  the  assumption  that  the  nature  of  the  world  admits  S  —  P. 
Because  reality  does  not  in  our  knowledge  exclude  S  —  P,  we 
take  reality  as  one  existing  condition  of  S  —  P,  and  we  assume 


l88  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

not  only  that  the  rest  may  be  found,  but  also  that  they  are 
compatible  with  reality.  In  this  lowest  and  barest  sense  of 
possibility  it  is  really  wrong  to  call  S  —  P  possible.  It  is 
better  to  say,  We  do  not  know  that  S  — P  is  impossible.* 

Between  these  extremes  come  many  degrees.  In  the 
hypothetical  judgment  about  S  — P  we  may  not  know  the 
special  conditions  of  S  —  P,  but  we  may  know  a  smaller  or 
greater  amount  of  them,  and,  where  we  are  ignorant,  we  may 
have  more  or  less  reason  to  make  an  assumption.  And  in 
respect  to  the  partial  existence  of  these  conditions,  our  know- 
ledge admits  of  many  stages,  and  we  make  assumptions  with 
grounds  that  may  vary  almost  indefinitely.  We  should  gain 
nothing  here  by  dwelling  on  these  varieties,  and  prefer  to  give 
some  simple  illustrations. 

§  14.  Are  disembodied  spirits  possible  ?  Let  us  agree  to 
take  the  most  unfavourable  view  for  the  sake  of  argument. 
We  have  no  direct  experience  of  the  existence  of  such  spirits, 
and  the  question  is  whether  we  can  call  them  possible.  We 
know  no  conditions  which  would  give  the  result.  We  have  no 
reason  to  think  such  imagined  conditions  compatible  with  the 
real  nature  of  things.  On  the  other  hand  we  can  not  reject  the 
idea  as  impossible,  since  we  have  no  right  to  affirm  "  It  is 
incompatible  with  the  nature  of  things."  We  should  content 
ourselves  with  saying,  "Your  proposed  assertion  is  not 
certainly  false,  but  there  is  no  ground  for  thinking  it  true. 
Our  ignorance  is  forced  to  admit  a  *  bare  possibility,'  but  it 
gives  not  the  very  smallest  reason  for  entertaining  that  idea  as 
real.  And  such  bare  possibilities,  we  have  seen,  are  none ; 
they  "  are  idle  frivolities,  that  have  no  place  in  the  minds  of 
reasonable  men." 

The  case  we  have  given  is,  as  we  have  given  it,  an  example 
of  the  lowest  sense  of  "  possible."  Let  us  go  a  step  higher. 
"  It  is  possible  that  some  of  the  planets  are  inhabited."  We 
have  here  the  hypothetical  judgment  that  under  certain 
conditions  life  would  result ;  and  to  some  extent  we  know 
these  conditions,  while  we  supplement  our  ignorance  by 
assumptions  for  which  we  have   reasonable   ground.     These 

*  We  rest  our  assertion  on  a  privative  judgment.  Cf.  Chap.  III. 
§  8,  and  p.  198. 


Chap.  VII.]  THE   MODALITY   OF   JUDGMENTS)^^  ^       1 89 

Special  conditions  again  are  in  various  planets  known^^exist 
in  part  and  in  different  amounts.  Our  judgment  that  this  or 
that  planet  may  be  tenanted  thus  varies  through  different 
degrees  of  possibility,  according  to  the  amount  of  this  partial 
existence. 

But  now  take  the  assertion  "  That  coin  may  have  given 
head."  Here  we  know,  on  the  one  hand,  special  conditions 
which  must  exhibit  head,  and  we  know  on  the  other  hand  that 
part  of  these  conditions  really  exists.  This  is  possibility  in  its 
highest  form. 

§  15.  We  have  noticed  that  possibility  may  stand  not  on 
fact  but  on  supposition.  If  a  coin  had  three  sides,  then  it 
would  be  possible  that  neither  head  nor  tail  should  be  upper- 
most. There  is  here  no  vital  change  in  the  meaning  of 
"  possible."  For  the  real  basis  is  supposed  to  exist,  and  the 
possible  is  subject  to  the  supposition.  But  we  should  not  here 
say  that  S  —  P  is  possible  ;  we  can  not  strictly  go  beyond  "  It 
would  be  possible."  It  is  possible,  if  by  a  fiction  of  thought 
you  treat  the  unreal  as  if  it  were  real,  or  the  unknown  as  if 
it  were  known.  We  must  distinguish  such  hypothetical  from 
actual  possibility.  For,  just  as  we  more  commonly  imply  that 
the  necessary  exists,  so  we  imply  and  must  ordinarily  even  be 
taken  to  assume  that  the  ground  of  the  possible  is  actual  fact 
and  not  merely  supposed. 

§  16.  We  have  now  discussed  the  meanings  of  "possible" 
and  "  necessary,"  so  far  as  to  see  that  both  are  forms  of  the 
hypothetical.  And  with  this  conclusion  we  have  anticipated 
the  result  of  our  second  enquiry,  Does  logical  modality  exist 
in  fact  "i 

(ii)  We  saw  long  ago  that  hypothetical  judgments,  as  such, 
are  not  true  in  rerum  natura.  Neither  the  subject,  nor  the 
predicate,  nor  again  the  connection,  need  exist  in  fact.  What 
is  true  of  fact  is  the  quality  that  forms  the  base  of  that  con- 
nection. The  junction  itself  may  be  non-existent  and  even 
impossible.  We  shall  verify  this  result  in  the  possible  and 
the  necessary. 

§  17.  {a)  We  have  seen  that  what  must  be  is  never  neces- 
sary save  on  the  hypothesis  of  some  condition.  We  have  seen 
that   this   antecedent,    and    the   consequence   which   follows. 


IQO  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

may  claim  no  existence  and  may  have  no  possibility.  The 
necessity  in  these  cases,  if  we  mean  the  necessary  connection 
of  the  elements,  does  not  exist  outside  our  ideas  ;  it  is  not 
true  of  fact. 
^And  again,  when  the  antecedent  and  with  it  the  conse- 
quence have  actual  existence,  and  appear  in  a  relation  which 
is  clearly  the  counterpart  of  logical  necessity,  the  same  result 
holds.  We  saw  that  the  difference  between  the  cause  of 
knowledge  and  the  cause  of  existence  staggers  our  assump- 
tions. And  even  when  the  two  seem  to  us  to  coincide,  how 
can  we  assume  that  they  are  ever  identical  ?  It  is  a  great  thing 
to  say  that  what  is  true  in  thought  must  hold  in  fact.  But 
it  is  something  more  to  maintain  that  thinking  and  existence 
appear  as  two  sides  of  a  single  reality,  and  to  insist  that  every 
logical  process  must  be  found  in  fact,  and  that  all  real 
connection  is,  if  we  could  see  it,  a  logical  process.  We  shall 
recur  to  these  questions  in  a  later  Book.  For  the  present  we 
may  repeat  that,  if  such  a  doctrine  is  tenable  in  metaphysics, 
it  can  not  be  supported  in  a  logical  treatise.  The  objections  it 
calls  forth,  if  they  could  be  disposed  of,  could  be  disposed  of 
only  by  a  complete  revolution  of  our  current  doctrine  as  to 
mind  and  things. 

For  logic  the  necessary  must  remain  the  hypothetical. 
Facts  for  logic  giust  be  facts  that  are  and  that  never  mitst  be. 
The  real  connection  which  seems  the  counterpart  of  our  logical 
sequence,  is  in  itself  not  necessary.  It  is  necessary  for  us, 
when  in  ideal  experiment  we  retrace  the  process  of  actual 
fact.  But,  at  least  in  logic,  we  must  not  assume  that  our 
ideal  relation  is  the  bond  of  existence.  The  ideal  compulsion 
of  logical  necessity  is  as  strong  where  the  premises  are  known 
to  be  false,  and  the  antecedent  can  not  be  believed  to  exist, 
as  where  we  start  from  categorical  truths  and  pass  from  them 
to  a  categorical  conclusion.  If  in  both  these  cases  there  is 
logical  necessity,  how  can  we  ever  be  safe  in  assuming  that 
such  necessity  is  found  in  existence  ? 

§  1 8.  {b)  And  when  we  pass  from  the  necessary  to  the 
possible,  our  conclusion  remains.  The  possible,  as  such,  exists 
nowhere  at  all  but  in  the  heads  of  men.  The  real  is  not 
possible  unless  for  a  moment  you  think  of  it  as  unreal.    When 


Chap.  VII.]  THE   MODALITY   OF   JUDGMENTS.  IQI 

the  possible  becomes  real  it  ceases  at  once  to  be  a  mere 
possibility.  For  metaphysics  I  will  not  deny  that  the  possible 
might  bear  another  meaning.  But  for  logic,  wherever  a  fact 
appears,  a  possibility  vanishes.  It  is  not  merely  that  the 
possible  is  confined  within  the  limits  of  human  thinking.  It 
can  not  exist  outside  the  domain  of  human  doubt  and  human 
ignorance. 

We  have  seen  that  to  say  "  S  —  P  is  possible,"  means,  "  S  —  P 
would  follow  under  certain  conditions,  some  at  least  of  which 
are  not  known  to  be  present."  And  at  this  stage  of  our 
enquiry,  we  may  say  at  once  that  the  sequel  of  such  a  hypo- 
thetical judgment  can  not  be  taken  to  have  actual  existence. 
The  antecedent  is  not  fact,  the  connection  is  not  fact,  and 
the  consequence  is  not  fact.  Or,  if  they  are  fact,  their 
"  factual "  character  must  be  either  unknown  or  put  out 
of  our  minds,  when  we  treat  them  as  possible.  If  we  knew 
the  reality  we  should  make  no  supposals  ;  or,  if  we  made 
them,  we  should  know  that  they  were  made  and,  as  such,  did 
not  exist. 

§  19.  Common  usage  enforces  our  conclusion.  The 
accused  obviously  is  guilty  or  is  not  guilty  (Sigwart,  228). 
But  we  say  "  It  is  possible  he  may  be  either."  That  is  grossly 
false,  if  you  take  it  as  asserting  about  the  fact,  A  fact  is  not 
and  can  not  be  an  alternative.  The  possible  existence  of  both 
guilt  and  innocence  is  relative  to  our  knowledge  ;  it  exists 
only  in  our  heads,  and  outside  them  has  no  meaning.  A  ship 
has  sailed  from  Liverpool  for  America,  and  we  say  "  It  may 
have  arrived  in  New  York,  or  again  it  may  be  at  the  bottom 
of  the  sea."  If  you  make  this  statement  of  the  actual  fact,  it 
can  not\y^Xx\XQ^.  It  is  not  possible  that  a  ship  should  be  in  two 
places  at  once.  It  must  actually  be  somewhere  ;  and,  being 
actually  there,  it  is  not  possibly  elsewhere,  nor  even  possibly 
where  it  is.  The  possibility  is  nothing  beyond  a  supposition 
founded  on  our  real  or  hypothetical  ignorance.  Outside  that 
ignorance  and  that  supposition  it  is  not  anything  at  all. 

§  20.  We  have  now  shown  in  the  first  place  that 
"  necessary  "  and  "  possible  "  are  both  hypothetical.  We 
have  seen  in  the  second  place  that,  at  least,  for  logic,  they  do 
not  exist,  as  such,  in  the  world  of  fact.     It  remains  to  show 


192  THE   PRINCIPLES   OF  LOGIC.  [Book  I. 

that,    although    "subjective,"    they  must  rest   on  a  basis  of 
categorical  assertion  about  reality. 

(iii)  We  have  only  to  recall  the  doctrine  we  reached  in 
our  Second  Chapter,  to  perceive  at  once  the  truth  of  this 
conclusion.  ^jsjyVe  saw  there  that  all  judgment  in  the  end  was 
categorical.  The  basis  of  the  hypothetical  must  be  fact,  and 
without  that  basis  the  judgment  would  be  false. 

{a)  We  need  give  ourselves  no  pains  to  verify  this  result 
■in  the  case  of  necessity.  We  have  seen  that  "S  — P  is  a 
necessary  truth  "  means  "  S  — P  follows  from  something  else."' 
This  something  else  need  not  be  fact,  and,  where  it  is  fact, 
that  can  not  be  assumed  to  make  any  difference  to  the  ideal 
connection.  We  can  not  say  "In  fact  S  —  P  really  is  a 
necessary  consequence  as  such."  But,  the  connection  being 
hypothetical,  it  on  the  other  hand  demands  a  basis  which  is 
categorical.  HAll  necessity  affirms  a  real  ground  explicit  or 
implicit.  It  thus  so  far  has  actual  existence,  not  in  itself, 
but  indirectly  and  simply  in  its  ground  (Chap.  IL). 

§  21.  When  we  come  {b)  to  the  possible,  we  are  tempted 
to  think  it  has  less  actuality  than  belongs  to  the  necessary, 
since  a  part  of  its  conditions  remains  unspecified.  But,  un^Jj 
less  we  imply  that  the  antecedent  of  the  necessary  exists  in  r 
fact,  such  a  comparison  would  be  illusory.  In  neither  case 
can  we  assurne  that  antecedent  or  consequent  exists  ;  and 
when  we  pass  from  what  must  be  to  what  only  may  be,  the 
ground  of  the  judgment  seems  in  either  case  to  be  equally 
real. 

In  the  merest  hypothetical  possibility  we  have  an  assertion 
about  actual  fact.  We  affirm  the  necessity  of  S  —  P  following 
from  abcdy  conditions  a  part  of  which  is  supposed.  And 
in  this  we  attribute  the  base  of  that  connection  to  ultimate 
reality.  But  in  an  ordinary  assertion  of  possibility  we 
imply  the  existence  of  a  part  of  abed,  and  thus  make  another 
statement  about  fact.  What  we  do  in  a  case  of  so-called 
bare  possibility  again  is  this.  We  first,  on  the  strength  of 
a  privative  judgment  (§  13),  conclude  that  the  conditions 
are  compatible  with  reality.  We  then  get  the  existence  of 
a  part  of  these  unspecified  conditions  by  taking  the  real 
{because  it  is  compatible)  as  a  joint  condition.      Thus  reality. 


Chap.  VII.]  THE   MODALITY   OF  JUDGMENTS.  193 

taken  in  some  unknown  character  and  passing  into  the  con- 
ditions, gives  partial  existence  unknown  to  the  antecedent ; 
while  the  same  reality,  in  another  character,  then  guarantees 
the  hypothetical  sequence  of  S  -  P.  We  thus  in  the  end  (what- 
ever we  may  think  of  them)  have  two  categorical  assertions. 

In  "  A  disembodied  spirit  is  possible  "  we  start  by  denying 
that  it  is  impossible.  This  judgment  rests,  first,  on  the  as- 
sumption that  the  real  has  an  actual  unknown  quality,  which, 
in  the  second  place,  if  you  take  it  together  with  other  un- 
specified conditions,  makes  a  hypothetical  antecedent  from 
which  "  disembodied  spirit  "  follows  as  a  consequence.  As  the 
ground  of  this  second  judgment  we  have  to  attribute  another 
unknown  quality  to  the  real  to  serve  as  the  basis  of  the 
hypothetical  connection.  We  have  thus  two  assertions  about 
the  nature  of  things. 

§  22.  Let  us  now  take  an  instance  of  rational  possibility. 
If  we  say  "  It  is  possible  A  holds  the  ace  of  trumps,"  we  know 
there  are  conditions  which  would  give  this  result.  Such  or 
such  an  arrangement  of  the  pack,  such  or  such  adjustments  of 
the  muscles  in  the  person  who  cuts  and  the  person  who  deals, 
must  give  the  ace  to  A.  The  ground  of  this  judgment  consists 
in  mechanical  and  other  laws,  in  accordance  with  which  the 
result  would  follow.  These  laws  we  regard  as  qualities  of  the 
real,  and  this  is  one  of  our  assertions.  We  next  affirm  that  an 
event  has  happened,  viz.  the  dealing  of  the  pack,  which 
presents  in  fact  a  certain  part  of  our  antecedent ;  in  other 
words,  which  gives  reality  to  our  supposed  conditions  to  a 
certain  point  and  within  a  limit.  The  antecedent  is  not 
actual  in  that  full  and  especial  form  which  gives  the  ace  to  A, 
but  it  is  there  in  that  outlined  and  partial  character  which 
gives  the  ace  to  some  one  player. 

Everywhere,  where  we  say  that  S  —  P  is  possible,  we  assert 
a  real  possibility  of  S  — P.  We  must  assume  a  fact  which 
actually  is,  though  it  is  not  S  —  P.  And  we  assume  that  this 
fact  would  under  some  conditions  give  us  S  —  P.  That  is,  we 
categorically  assert  the  ground  of  an  hypothetical  judgment ; 
and  again  we  categorically  assert  the  existence  of  a  fact  which 
forms  part  of  the  antecedent.  These  two  positive  assertions 
can  everywhere  be  found  in  the  most  guarded  statement  about 

o 


194  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

an  actual  possibility ;  and  the  former  is  required  for  mere 
hypothetical  possibility. 

We  have  now  accomplished  the  third  task  we  set  before  us. 
We  have  shown  that  the  necessary  as  well  as  the  possible 
has  a  basis  in  fact  and  depends  upon  experience.  A  modal 
judgment  has  to  make  an  assertion  about  reality.  But  the 
judgment  itself  expresses  a  truth  which  is  not  a  fact. 
Modality  is  but  hypothetical,  and  hypothetical  connections 
exist  only  in  our  thoughts. 

§  23.  There  are  various  points  in  connection  with  the 
subject  which  claim  our  attention.  We  are  accustomed  to 
hear  of  "capacities  " and  " faculties,"  and  to  use  such  phrases 
as  "  potential  energy,"  with  but  little  regard  for  their  actual 
meaning.  The  "  potential "  is  regarded  as  something  real, 
stored  up  outside  existence,  which  hereafter  may  emerge  in 
the  world  of  fact.  This  deplorable  piece  of  effete  metaphysics 
takes  a  leading  place  in  popular  versions  of  the  truths  of 
physics.  Potential  energy  of  course  as  such  has  no  real 
existence.  It  is  merely  the  consequence  in  a  hypothetical 
judgment  where  the  conditions  are  not  all  taken  as  actual. 
It  would  be  better  to  say,  "Though  there  is  no  energy, 
there  is  something  actual  which  exists  as  the  real  possi- 
bility of  energy."  But  even  this  correction  leaves  a  residue 
of  error. 

In  strictness  of  speech  a  real  possibility  of  S  -  P  can  not 
exist  as  such.  It  should  mean  that  reality  which,  if  you  place 
it  in  an  ideal  construction,  developes  S  —  P  as  a  consequence. 
Itself  is  fact,  and  the  attribute  at  the  base  of  the  hypothetical 
judgment  again  is  fact :  but  that  judgment  with  its  elements 
can  not   be   taken   as   fact.     We  are  met   by  this  dilemma. 

^  Apart  from  the  judgment  the  real  is  mere  fact  and  has  no 
,  potentiality ;  but  within  the  judgment  the  reality  itself  has 
/ceased  to  be  real.  It  has  taken  its  place  in  a  mental  con- 
'  struction.  Unless  you  are  prepared  to  make  ideal  elements 
determining  forces  in  the  processes  of  nature,  you  can  not 
properly  believe  in  real  possibilities.  And  I  think,  upon  any 
metaphysical  theory,  it  would  be  better  to  find  some  other 
expression. 

§  24.  But  I  shall  hear :  "  Conditions  are  surely  real.    Before 


Chap.  VIL]  THE  MODALITY  OF  JUDGMENTS.  195 

life  began  its  conditions  could  be  present.  And  the  real  possi- 
bility being  a  condition,  as  such  you  must  allow  it  to  exist." 
In  the  above  I  see  nothing  but  the  same  mistake,  f  A  con- 
dition as  such  can  not  be  said  to  exist.  A  condition  is  an 
element  in  a  hypothetical  judgment  and,  outside  that  judgment, 
it  is  no  conditionTl  If  you  say,  "A  exists  and  is  an  actual 
condition  of  B,"  you  are  speaking  inaccurately.  What  real 
bond  corresponds  to  your  phrase }  B  is  not  in  existence,  and 
if  the  other  conditions  do  not  appear,  it  will  not  exist.  And 
yet  you  say,  "  A  is  one  of  its  conditions."  If  you  wish  to  be 
accurate  you  should  say,  "  A  is  something-which,  if  taken  from 
existence  and  placed  within  an  ideal  construction,  mentally 
gives  rise  to  B."     All  beyond  is  unwarranted. 

A  condition  ex  vi  termini  does  not  as  such  exist ;  and  to . 
define  the  cause  as  "  the  sum  of  the  conditions  "  is  to  commit 
a  serious  metaphysical  mistake.  It  is  saying,  "  The  reality 
which  gives  rise  to  reality  is  made  up  by  adding  mere  ideas 
together."  *  But  the  cause  must  be  fact,  and  its  effect  must 
be  fact.  We  should  do  better  to  call  the  cause  the  meeting  of 
elements  which,  in  the  moment  of  their  union,  begin  a  process 
which  issues  in  the  change  we  call  the  effect.  An  actual 
union  of  actual  elements  is  the  cause.  Each  element  by 
itself  and  apart  from  this  union  is  not  even  a  condition.  It 
becomes  a  condition  when  you  place  it  ideally  in  union  with 
others.  But,  in  order  to  do  that,  you  must  make  it  an  idea.y  ? 
In  its  character  of  condition  it  must  so  far  cease  to  be 
fact. 

I  am  far  from  suggesting  that  the  want  of  accuracy  I  have 
just  been  noticing  is  always  error.  The  phrases  "  potential  " 
and  "  condition "  and  "  possibility "  may  be  harmless  and 
useful.  We  ought  all  to  be  able  to  employ  them  safely.  But 
I  fear  that  too  often  the  case  is  otherwise.  Too  often  they 
prove  mere  engines  of  illusion,  drowsy  sops  thrown  down  to 
make  reason  slumber.  If  we  believe  in  something  that  neither 
is   nor  is  not,  but  rules  some  strange  middle-space  between 

*  Of  course  the  word  su7n  again  is  open  to  criticism.  It  implies  a 
theory  of  the  union  of  the  elements,  which  certainly  can  not  be  taken 
for  granted.  But  to  clear  up  this  point  a  long  digression  would  be 
wanted.   There  are  some  remarks  on  causation  in  Book  III.  II.  Chap.  II. 

O   2 


196  THE  PRINCIPLES  OF  LOGIC.  [Book  I. 

existence  and  nothingness,  let  us  at  least  have  courage  to 
profess  our  opinion.  Do  not  let  us  use  words  in  using  which 
we  take  refuge  from  doubt  in  blind  ambiguity. 

§  25.  It  was  blind  ambiguity  and  little  beside  that  lay  at 
the  root  of  a  controversy  we  remember.  Amongst  those  who 
vexed  themselves  and  others  with  disputes  on  the  "  Permanent 
Possibilities  of  Sensation,"  how  many  adopted  the  obvious 
course  of  asking  what  lay  hid  in  this  spell  ?  We  know  now 
that  a  r^^/ possibility  means  something  which,  in  itself  and  in 
fact,  is  no  possibility,  but  must  be  something  actual.  It  is  a 
veritable  fact  which  actually  exists  ;  and  to  this  we  must  add 
here  the  idea  of  permanence,  I  suppose  this  means  that  our 
actual  fact  has,  against  something  else,  at  least  a  relative 
duration  and  freedom  from  change.  But  now  what  is  this 
real  or,  I  should  say,  these  reals,  which  do  not  change,  and 
which  an  attribute  of  the  reality  guarantees  to  produce  the 
consequence  of  sensation,  so  soon,  that  is,  as  you  have 
transformed  them  into  ideas,  and  placed  them  within  ideal 
constructions }  Are  they  real  things,  as  distinct  from  sen- 
sations, or,  if  not,  what  are  they?  I  do  not  say  that  the 
asking  this  question  is  enough  to  explode  the  theory  of 
J.  S.  Mill.  I  will  say  that  the  answer  to  it,  however  it  is 
answered^  must  alter  at  least  the  statement  of  that  theory,  and 
change  at  least  some  of  the  points  in  dispute. 

I  must  be  pardoned  for  seeing  in  another  use  of  this 
delusive  phrase  an  ambiguity  which  threatens  the  conclusion. 
If  there  are  difficulties  in  the  way  of  making  pleasure,  in  the 
sense  of  atomic  and  momentary  feelings,  the  end  of  life,  can 
we  be  said  to  escape  them  if  we  say  Happiness  is  the  end,  and 
if  Happiness  is  defined  as  a  permanent  possibility  of  pleasant 
feeling  ?  We  are  met  by  the  objection,  If  the  end  is  pleasure 
then  it  surely  must  lie  in  actual  pleasure.  But  if  it  lies  in 
actual  pleasure,  it  can  hardly  lie  in  mere  possible  pleasure. 
Either  the  end  is  pleasure  present  and  actual,  such  pleasure 
again  as  has  a  quality  (itself  also  pleasure)  which  guarantees 
a  hypothetical  result  of  ideal  pleasure,  and  this  present 
pleasure  is  also  permanent — either  this,  I  say,  or  Hedonism  is 
given  up,  for  something  not  pleasure  is  made  the  end.  Here 
again  I  must  venture  to  make  the  remark  that  the  answer  to 


Chap.  VII.]  THE   MODALITY   OF  JUDGMENTS.  I97 

the   objection   must  modify   at   least   the   statement   of  the 
doctrine. 

§  26.  We  may  turn  from  these  criticisms  to  a  positive  result 
laid  down  by  Sigwart  (182,  227),  and  which  our  discussion  of 
possibility  should  have  served  to  make  clear.  The  particular 
judgment,  in  the  end  and  really,  we  found  to  be  nothing  but 
a  hypothetical  in  which  the  conditions  remained  imperfect 
(Chap.  II.).  In  the  problematic  form  of  judgment  we  once  again 
encounter  the  particular.  The  one  is  the  other  under  a  disguise 
which  disappears  before  our  scrutiny.  The  particular  judgment 
"  Some  S  is  P  "  is  the  same  as  the  judgment  "  S  may  be  P." 
The  assertion  that  S  does  actually  exist  is  not  contained  in 
the  particular  judgment,  any  more  than  it  is  in  the  problematic. 
"  Some  S  is  P  "  asserts  no  more  than  that,  S  being  given  in 
ideal  connection  with  other  conditions,  of  which  conditions 
some  part  is  assumed  or  supposed  to  be  actual,  then  P  will 
follow.  And  this  is  precisely  the  sense  of  "  S  may  be  P." 
Both  are  imperfect  hypothetical  judgments,  and  both  are 
founded  on  a  basis  of  fact  believed  in  or  supposed  (§  15). 

§  27.  Reality  in  itself  is  neither  necessary,  nor  possible, 
nor  again  impossible.  These  predicates  (we  must  suppose  in 
logic)  are  not  found  as  such  outside  our  reflection.  And  to 
a  knowledge  and  reflection  that  had  command  of  the  facts 
nothing  ever  would  be  possible.  The  real  would  seem 
necessary,  the  unreal  would  seem  impossible. 

The  impossible  is  that  which  must  be  unreal.  We  might 
call  it,  if  we  chose,  one  kind  of  the  necessary.  When  we  say  of 
S  —  P  that  it  can  not  exist,  we  do  not  merely  mean  that  in  ideal 
experiment  the  suggestion  of  S  — P  directly  vanishes.  We 
suppose  for  a  moment  that  S  --  P  is  real.  Then  on  that  hypo- 
thesis we  see  that  the  conditions  from  which  alone  S  —  P  would 
follow  are  directly  or  indirectly  incompatible  with  the  real. 
The  real,  if  changed  in  ideal  construction  so  as  to  afford  the 
conditions  of  S  —  P,  is  changed  in  such  a  way  as  to  cease  to 
be  itself  The  alteration  removes  some  attribute  that  we  assign 
to  the  real ;  and  this  attribute,  in  our  reflection,  by  means  of  its 
exclusion  of  other  possibilities,  thus  generates  the  impossible 
and  becomes  the  necessary. 

Impossibility  and  necessity  are  correlative  ideas.     They 


198  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

emerge  together.^  The  real  does  not  seem  necessary  until  it  has 
excluded  what  is  incompatible,  and  reasserted  the  attribute 
which  is  the  ground  of  the  exclusion.  Because  of  this  attribute 
nothing  else  can  be,  and  the  attribute  must  be  because  nothing 
else  is.  The  unreal  again  is  not  impossible  until  we  have  seen,  not 
merely  that  it  fails,  but  that  its  supposed  success  would  destroy 
what  is,  and  what  must  be  because  its  opposite  is  excluded. 

§  28.  These  ideas  suggest  a  number  of  difficulties.  In  a 
later  book  we  must  return  to  one  of  them,  and  may  content 
ourselves  here  with  a  brief  indication.  The  impossible  we  see 
must  always  imply  a  positive  quality,  known  or  assumed  to 
belong  to  the  real.  If  X  is  impossible,  this  means  and  must 
mean  that  an  actual  X  would  remove  by  its  presence  some 
positive  attribute  we  take  to  be  real. 

This  bears  on  a  point  which  already  has  engaged  us 
(§§  13,  21).  The  possible  may  be  taken  as  anything  whatever 
which  is  not  real  nor  yet  impossible.  We  objected  to  this 
process,  as  frivolous  in  its  result  and  insecure  in  its  method. 
The  method  is  insecure,  since  it  passes  from  the  absence  of 
known  incompatibility  to  the  assumption  of  compatibility. 
We  take  X  to  be  compatible,  if  the  real,  as  we  know  it,  will 
pass  unabridged  into  a  set  of  conditions  which  give  X  as  a 
consequence.  Again,  so  far  as  we  know,  X  is  not  incompatible, 
when  the  suggestion  of  X  as  an  attribute  of  the  real  calls 
forth  no  answer  affirmative  or  negative.  And  the  doctrine 
we  object  to  passes  direct  from  want  of  incompatibility  to 
compatibility.  In  the  one  case  X  is  possible,  since  it  follows 
from  conditions  a  part  of  which  is  supplied  by  the  real.  But 
in  the  other  case  we  can  say  nothing  about  reality,  unless 
we  make  an  enormous  assumption. 

§  29.  We  offer  our  suggested  X  to  the  real,  and  the  real 
is  passive :  X  is  not  excluded.  This  privative  judgment,  if 
we  wish  to  understand  it,  must  be  reduced  to  an  ordinary 
negative  where  a  positive  quality  in  the  subject  rejects.  What 
is  the  positive  quality  here  ?  It  is  the  mental  presence  of  the 
real  with  such  and  such  attributes.  Now  even  the  smallest 
addition  to  these  present  attributes  is  an  alteration  of  the  real, 
as  we  have  it  in  our  minds,  against  which  it  asserts  itself  in 
the  character  it  bears  at  the  actual  moment.     In  other  words. 


Chap.  VII.]  THE   MODALITY   OF  JUDGMENTS.  I99 

the  base  of  our  assertion  that  X  is  not  rejected  by  the  real,  is 
the  assumption  that  the  real  differs  in  no  point  from  the  real 
as  at  this  moment  it  is  present. 

Now  it  is  one  thing  to  say  "  Whatever  I  judge  true  holds 
good  of  reality,"  and  another  thing  to  say  "  What  I  fail  to  judge 
true  is  absent  from  reality."  And  there  is  this  very  great 
difference  between  them.  In  the  first  case  we  assume  that, 
whatever  else  may  be,  at  least  so  much  is  true.  In  the  second 
we  go  so  far  as  to  say  that  what  we  have  in  our  minds  is 
co-extensive  with  reality.  But,  if  we  hold  to  this,  we  ought  to 
go  further.  What  the  real  does  not  exclude  is  not  possible,  it 
is  actual  and  necessary  (p.  143).  And  if  we  shrink  from  this 
assertion,  ought  we  to  maintain  that  X  is  even  possible  ? 
J\  30.  The  mistake  is  apparent.  A  privative  judgment 
(as  we  saw  in  Chapter  III.)  is  not  true  of  a  subject,  if  that 
subject  is  confined  to  something  without  the  sphere  of  the  pre- 
dicate. It  then  becomes  obviously  frustrate  and  unmeaning. 
You  can  not  predicate  absence  unless  you  predicate  the  posi- 
tive space  from  which  the  absent  is  lacking  (Chap.  III).  We 
shall  find  that  this  holds  good  of  ultimate  reality.  To  say  of 
it,  "  It  is  without  the  rejection  of  X,"  is  to  say  of  it  something 
which  has  no  meaning  unless,  so  to  speak,  the  place  left  empty 
by  this  mere  privation  is  occupied  by  a  positive  attribute. 
We  ought  to  be  able  to  say  There  is  a  quality  the  presence  of 
which  guarantees,  or  goes  to  guarantee,  the  absence  of  the 
exclusion  of  X.  But  this  quality  would  obviously  be  either 
the  presence  or  compatibility  of  X.  It  is  on  the  ground  of  this 
presence  or  compatibility  that  we  ought  to  assert  the  possibility 
of  X.     For  otherwise  we  fall  into  circular  argument. 

I  will  give  an  illustration.  Suppose  I  were  to  say  that  an 
isosceles  triangle  with  three  unequal  angles  is  certainly  possible, 
and  possible  because  it  is  not  ^impossible.  The  universal 
triangle,  so  far  as  I  am  supposed  to  know  it,  tells  me  nothing 
about  the  nature  of  the  isosceles.  On  the  privative  judgment 
that  the  universal  triangle  does  not  reject  my  idea,  I  call  it 
possible.  Is  not  this  absurd  }  It  is  absurd,  because  a  privative 
judgment,  where  the  subject  is  left  entirely  undetermined  in 
respect  of  the  suggestion,  has  no  kind  of  meaning.  Privation 
gets  a  meaning,  where  the  subject  is  determined  by  a  quality 


200  THE   PRINCIPLES  OF  LOGIC.  [Book  I. 

or  an  environment  which  we  have  reason  to  think  would  give 
either  the  acceptance  or  the  rejection  of  X.  But,  if  we  keep 
entirely  to  the  bare  universal,  we  can  not  predicate  absence, 
since  the  space  we  call  empty  has  no  existence. 

§  31.  Or  if  our  privative  judgment  has  a  meaning,  then  it 
has  a  false  meaning  (Chap.  III.).  It  rests  on  a  confusion  between 
the  universal  and  its  psychological  existence.  We  take  the  idea, 
as  we  find  it  existing  within  our  minds  as  a  psychical  event, 
and  then  confound  the  determination  it  so  gets  with  its  logical 
qualities.  We  say  Here  is  a  fact,  and  we  can  not  find  that  it 
does  reject  X.  But  the  answer  is  simple.  In  the  first  place 
we  have  the  reductio  ad  absurdum.  Since  the  real  has  a  quality 
on  the  ground  of  which  it  must  accept  or  decline  every  possible 
suggestion  (Chap.  V.)  ;  and  since  the  real  here  ex  hyp.  does 
not  decline,  it  therefore  must  accept.  X  is  not  possible,  it  is 
actual  and  necessary.  In  the  next  place  we  directly  deny  the 
premise.  In  your  experiment  you  have  not  got  the  reality, 
and  you  ought  to  know  that  you  have  not  got  it.  If  you  wish 
to  determine  your  empty  universal  so  as  to  get  an  answer  in 
regard  to  X,  you  have  nothing  to  do  with  the  psychological 
setting  of  this  universal.  The  psychical  environment  is  not 
the  space  which,  in  respect  to  X,  must  be  full  or  empty.  It 
is  quite  irrelevant  and  must  be  discarded.  You  must  fill  out 
your  idea  by  adding  to  its  content.  When  the  content  is 
supplied  to  such  an  extent  that,  in  saying,  ^'  Rejection  of  X  is 
still  absent,"  you  mean  that  some  of  the  conditions  of  X  are 
already  present — when  you  mean  that  there  are  qualities 
which  do  afiect  the  prospects  of  X,  that  a  part  of  that 
attribute,  which  when  complete  will  accept  or  reject  X,  is 
already  there  and  that  part  is  favourable — then  I  admit  you 
may  found  possibility  on  your  privative  judgment.  The  com- 
plaint I  make  is  that  your  proceeding  is  frivolous.  You  have  in 
your  hands  the  positive  ground  on  which  your  judgment  is  based 
directly,  and  you  choose  to  proceed  in  a  way  which  is  indirect 
and  in  this  case  circular  (Chap.  V.  §  28). 

We  should  never  trust  a  privative  judgment  until  we  have 
seen  its  negative  form.  We"  should  never  trust  a  negative 
judgment  until  we  have  seen  its  affirmative  ground.  We 
.should  not  take  our  impotence  as  a  test  of  truth,  until  we  at 


y^ 


Chap.  VIL]  THE  MODALITY   OF  JUDGMENTS.  20I 

least  have  tried  to  discover  the  positive  counterpart  of  that 
failure.  The  observance  of  these  rules  might  preserve  us  from 
errors  which  sometimes  are  dangerous. 

The  relation  of  necessity  and  impossibility  to  our  mental 
impotence  is  a  subject  which  w^ould  carry  us  beyond  the 
present  volume.  We  shall  add  some  remarks  in  our  con- 
cluding Book.  In  the  present  chapter  we  have  yet  to  see  how 
modality  is  the  passage  from  judgment  to  reasoning.  But, 
before  we  indicate  that  transition,  we  must  rapidly  deal  with  a 
most  important  application  of  modality,  so  far  at  least  as  to 
show  its  connection  with  our  general  view. 

§  32.  If  Logic  professed  to  supply  a  method  for  the 
discovery  of  truth,  the  logician  could  not  mention  the  theory 
of  Probability  without  shame  and  confusion.  The  fruitful 
results  of  the  modern  rival  would  offer  themselves  in  damaging 
contrast  with  the  sterility  of  the  old  and  privileged  veteran. 
And,  where  a  true  view  of  the  claims  of  logic  makes  this 
contrast  impossible,  the  logician,  it  may  seem,  has  no  right  lo 
trespass  within  the  limits  of  another  science.  The  objection 
is  heightened  when  the  writer  on  logic  confesses  himself 
unacquainted  with  mathematics.  He  may  appear  in  this  case 
to  be  talking  about  things  of  which  he  knows  nothing. 

But  the  objection  rests  on  a  misunderstanding.  The 
principles  on  which  probabilities  are  reckoned,  the  actual 
basis  and  foundation  of  the  theory,  are  not  themselves  mathe- 
matical. Before  mathematics  can  deal  with  the  subject  some 
assumptions  are  necessary ;  and,  though  these  assumptions 
can  be  justified  by  their  results,  it  is  desirable  to  examine 
them  simply  by  themselves,  to  see  what  they  are  and  whether 
they  are  true.  An  enquiry  of  this  sort,  by  whomsoever  it  is 
made,  is  a  logical  enquiry. 

§  33.  Probability,  we  know,  has  to  do  with  possibilities. 
And  starting  from  this,  at  the  point  we  have  reached,  we  can 
go  at  once  to  an  important  result.  No  statement  we  make  / 
about  probabilities  can,. as  such,  be  true  of  the  actual  facts. 
This  is  half  the  truth,  and  we  must  not  forget  it  But  it  is  not 
more  than  half,  nor  is  it  even  the  half  best  worth  remembering. 
It  is  just  as  true  that  an  assertion  about  chances  does  make  an 


202  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

affirmation  about  reality.  Every  hypothetical  judgment,  we 
have  seen,  must  rest  upon  some  categorical  basis.  The  con- 
clusions we  have  adopted  enable  us  to  say  without  further  \ 
enquiry.  Any  theory  which  calls  the  doctrine  of  chances  J 
merely  "  objective,"  or  merely  "  subjective,"  is  certainly  false.  It 
is  a  vicious  alternative  which,  if  it  were  sound,  would  upset 
general  results  we  have  found  to  be  true,  and  which  is  con- 
trary to  the  special  facts  of  the  case. 

§  34.  I  shall  return  hereafter  to  the  consideration  of  this 
root-mistake,  but  it  is  better  to  begin  with  a  statement  of  the 
truth.      We  are  to  omit  the  subject  of  probability  in  general, 
and  confine  ourselves  to  the  particular  instance  of  that  which 
is  called  mathematical  probability.     And  the  point  which  first 
presents  itself  to  our  notice,  is  the  necessity  of  limiting  the  / 
possibilities.     Before  we  can  advance  a  single  step  we  must 
have  the  whole  of  the  chances  before  us.     This  exhaustive 
survey  may  rest  on  knowledge  or  on  arbitrary  assumption,  but 
it  is  always  presupposed.     The  calculation  of  chances,  in  a    / 
word,  must   be   based   on   a   disjunctive  judgment,  and  the  "^ 
hypothetical  assertions,   which    represent    the    chances,  take    * 
place  within  the  bounds  of  that  judgment.     But  disjunction,  as 
we  know  (Chap.  IV.),  implies  a  categorical  foundation.     This 
basis   of  fact   is   the   condition    of  our  assertions  about  the 
chances. 

§  35.  Take  a  simple  instance.  A  die  has  been  thrown 
without  our  knowledge,  or  is  now  about  to  be  thrown  before 
us.  As  a  previous  step  to  reckoning  the  chances  we  must 
make  some  categoric  statements.  We  must  be  able  to  say. 
The  die  will  fall  (or  has  fallen),  and  will  fall  beside  in  a  certain 
way.  It  must  have  one  side  up,  and  this,  whatever  else  it  is, 
will  at  least  be  not  other  than  all  these  six  sides.  It  must 
have  a  quality  determined  as  what  is  common  to  the  six,  and 
not  determined  as  what  will  be  none  of  them.  On  this 
categorical  foundation  all  the  rest  is  based,  and  without  it 
there  is  no  possibility  of  advance. 

This  result  has  a  most  important  application.     There  is  no-J^ 
probability  before  all  reality.      There  is  none  which  does  not 
stand  on  a  basis  of  fact  assumed  or  actual,  and  which  is  not  a 
further  developement  of  that  basis. 


Chap.  VII.]  THE   MODALITY   OF  JUDGMENTS.  203 

§  36.  We  have  seen  the  foundation  of  our  disjunctive 
judgment.  What  is  it  that  completes  it?  It  is  of  course 
the  setting  out  of  exclusive  alternatives.  These  alternative 
possibilities  are  given  us  in  the  various  hypothetical  judg- 
ments which  we  are  able  to  make  as  to  the  number  on  the 
face  which  we  know  is  lying  uppermost,  or  which  will  so  lie. 
We  have  now  a  disjunctive  judgment,  enclosing  an  exhaustive 
statement  of  exclusive  possibilities.  But  we  have  not  yet  got 
to  mathematical  probability.  To  reach  this  a  further  step  is  to 
be  made.  We  must  take  the  possibilities  all  to  be  equal,  or,  if 
they  are  not  equal,  we  must  make  them  comparable. 

§  37.  The  possibilities  must  all  be  equally  probable. 
What  does  this  mean  ?  It  means  that  there  is  no  more  to  be 
said  for  one  than  there  is  for  another.  The  possibilities  are 
each  a  hypothetical  result  from  certain  conditions  ;  and  these 
results  are  equal,  when,  in  the  first  place,  they  follow  each  from 
no  more  than  one  single  set  of  conditions,  and  when,  in  the 
second  place,  I  attach  no  more  weight  to  any  one  set  than  I 
do  to  the  others.  When,  in  short,  I  have  no  more  reason  for 
making  one  hypothetical  judgment  than  I  have  for  making 
any  other,  they  are  possible  alike  and  equally  probable. 

X  must  he  a  or  d  or  c.  X  qualified  by  certain  conditions 
would  be  a,  if  qualified  by  other  conditions  would  be  d,  and  so 
with  c.  If  in  my  knowledge  I  have  any  ground  for  taking  X 
in  one  set  of  conditions  rather  than  in  another,  then  a,  d,  and  c 
are  not  equally  likely.  If  such  a  ground  is  absent,  then  they 
are  equal.  Again,  if  X  will  give  a  with  a  single  set  of  con- 
ditions, and  d  or  c  with  more  than  one  set,  the  chances  are 
different  in  the  different  cases.    Otherwise  they  are  the  same.* 

§  38.  If  the  separate  alternatives  are  not  found  equal,  then 
we  must  either  give  up  our  attempt  to  reckon  chances,  or 
must  find  some  common  unit  of  value.  We  must  analyze  one 
possibility,  and  find,  perhaps,  that  its  final  result  is  really  two  ; 
or  that,  though  the  final  result  is  one,  it  will  follow  from  two  or 
three  sets  of  conditions,  and  hence  can  stand  for  two  or  three 
units.     In  these  cases  there  were  two  hypothetical  judgments 

*  Wolff  has  expressed  the  principle  very  well,  "  Probabilior  est  pro- 
positio,  si  subjecto  predicatum  tribuitur  ob  plura  requisita  ad  veritatem, 
quam  si  tribuitur  ob  pauciora." 


204  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

which  we  joined  in  one.  Again,  if  we  can  not  divide  the 
greater,  we  may  join  the  smaller.  By  considering  two  or 
more  alternatives  as  one,  we  raise  the  whole  to  a  unit  of 
higher  value. 

§  39-  Where  we  have  a  disjunction  the  alternatives  of 
which  are  equally  likely,  or  are  reduced  to  alternatives  which 
are  equally  likely,  we  can  state  the  chances.  Since  we  have 
the  same  ground  to  think  every  possibility  true,  the  probabi- 
lity of  each  is  just  the  same  quantity.  In  our  knowledge  they 
divide  the  actual  fact  between  them  equally.  The  reality  then 
we  represent  as  unity,  and  each  alternative  possibility  we 
represent  by  a  fraction,  of  which  the  denominator  is  the 
number  of  equal  alternatives,  and  the  numerator  is  one. 
Against  our  belief  in  the  general  fact  we  have  nothing  to  set. 
Against  any  one  of  its  developements  we  have  to  set  the  whole 
of  the  others. 

§  40.  Take  the  instance  of  the  die.  We  know  it  will  fall 
in  a  certain  way.  So  much  is  categorical,  and  we  have  now  to 
determine  the  further  possibilities.  What  are  the  conditions 
from  which  in  each  case  our  hypothetical  results  proceed  } 
They  are  first  the  general  character  of  the  fall,  those  positive 
and  negative  general  conditions  from  which  comes  a  fall  with 
one  of  the  six  faces  up,  and  no  more  than  one.  Do  these 
furnish  a  ground  for  making  one  fall  more  likely  than  others  ? 
Clearly  they  do  not. 

The  general  conditions,  which  we  have  considered  so  far, 
are  known  to  exist.  The  fact  must  take  place  in  such  a  way 
that  these  conditions  will  be  realized.  But,  beside  this  known 
element,  there  are  a  number  of  circumstances  about  which  we 
are  in  doubt.  The  particular  throw  must  be  the  result  of  one 
particular  position  of  the  die,  the  contraction  of  particular 
muscles  in  the  thrower,  and  the  character  of  the  surface  which 
receives  the  fall.  The  number  of  different  sets  of  conditions 
which  would  lead  to  the  result,  is  very  great,  and  in  part 
perhaps  unknown.  Still  this  makes  no  difference.  They  are 
all  at  least  known  or  assumed  to  be  compatible  with  the  reality, 
and  they  lead  indifferently  to  any  one  of  the  six  results. 
With  respect  to  each  face  we  have  exactly  as  much  reason 
to  think  it  uppermost,    as  we  have  to  think  any  other  face 


Ohap.  vii.j       the  modality  of^  judgments.  205 

uppermost.  The  chances  are  equal  ;  and  since  they  are  six, 
and  since  they  divide  the  sphere  of  a  single  unity,  they  are 
each  one-sixth.  We  have  a  certain  reason  to  expect  one  face, 
say  for  instance  four,  but  we  have  the  same  reason  five  times 
over  not  to  look  for  four. 

§  41.  Now  suppose  one  face  loaded.  The  final  possibilities 
are  still  six  in  number,  but  their  value  is  not  equal.  There 
are  more  sets  of  conditions,  which  would  lead  to  the  loaded 
face  being  downwards,  than  sets  which  would  bring  the 
opposite  face  into  the  same  position.  I  have  thus  more  reason 
to  look  for  one  than  I  have  to  expect  the  rest.  My  task  is 
now  to  get  a  fresh  unit  by  breaking  up  some  or  all  of  the 
possibilities.  If  I  succeed  in  this,  the  whole  will  again  be 
divided  into  fractions  expressing  the  respective  chances,  but 
these  fractions  will  be  unequal.  The  units  of  reason  to  look 
for  each  face  will  be  more  in  one  case  and  less  in  another. 

§  42.  The  above  is,  I  think,  the  entire  foundation  of  the 
doctrine  of  chances.  It  is  perfectly  simple  and  entirely 
rational.  It  need  not  appeal  as  a  warrant  for  its  existence 
to  those  splendid  successes  which  make  it  indispensable. 
Rightly  understood  its  principles  by  ti^emselves  are  abun- 
dantly clear  and  beyond  all  controversy. 

We  have  no  cause  and  no  right  to  follow  the  theory  even 
into  its  first  and  most  simple  applications,  but  we  can  not 
pass  over  an  important  point.  Where  we  can  not  determine 
numerically  the  conditions  of  different  possibilities  in  a  way 
that  is  direct,  we  can  proceed  indirectly.  For  example,  in 
the  case  of  a  loaded  die,  I  may  have  no  data  for  calculating 
the  chances,  since  I  may  not  have  accurate  knowledge  of  the 
conditions.  But  I  can  go  to  the  result  in  another  way.  I 
can  throw  the  die  a  number  of  times,  and,  setting  down  the 
numbers  for  every  face,  can  then  in  view  of  an  unknown  throw 
state  the  fractions  in  accordance  with  the  relations  of  these 
numbers.  But  this  inverse  process  implies  no  appeal  to  a 
different  principle. 

Let  us  perceive  its  nature.  I  assume  that  I  have  no  reason 
whatever  to  think  the  unknown  throw,  which  I  wish  to  deter- 
mine, different  from  the  rest.  I  therefore  take  it  as  simply  the 
same.     But  I  can  not  take  it  as  the  same  as  any  oney  for  then 


206  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

it  must  be  different  from  others.  It  is  therefore  the  same  in 
its  general  character,  with  possible  alternatives  which  fall 
within  the  data  supplied  by  the  actual  series.  It  remains  to 
reduce  these  possibilities  to  fractions. 

We  are  obliged  to  reason  from  effect  to  cause.  If  a  known 
cause  A  would  produce  a  given  effect,  and  if  we  have  no 
reason  whatever  to  believe  in  any  other  cause,  we  assume  we 
can  go  from  the  effect  to  A.  The  effect  we  are  considering  is 
a  certain  series,  and  the  question  is.  Do  we  know  the  one  cause 
which  would  produce  that  series  } 

I  hardly  think  we  do.  However  long  and  however  regular 
the  series  may  be,  we  can  never  say  that  there  is  one  and  but 
one  disposition  of  elements,  which  leads  and  must  lead  to  the 
series  we  have  seen.  And  if  we  could  say  this,  and  assume 
beside  that  the  unknown  throw  will  follow  from  this  deter- 
minate cause,  then  there  would  no  longer  be  any  probability  in 
the  case.  The  whole  thing  would  be  understood  and  certain. 
But  we  obviously  do  not  know  this  one  special  cause  which 
would  produce  our  series.  We  can  determine  no  more  than  its 
general  character.  It  must  be  such  a  cause  as  would  give  a 
series  possessing  certain  numerical  relations.  And  we  assume 
that  an  arrangement  of  which  we  can  say,  "  It  is  the  real  possi- 
bility, with  respect  to  any  throw,  of  chances  disposed  in 
those  numerical  relations,"  is  such  a  cause.  It  is  therefore 
probable  that  the  series  is  the  effect  of  this  cause.  And  since 
(by  another  assumption)  we  have  no  reason  to  believe  in  any 
other  cause,  it  is  certain  that  the  series  has  resulted  from  this 
cause.  And  since  again  we  assume  that  the  unknown  throw 
has  a  general  character  the  same  as  that  possessed  by  the 
series,  we  proceed  without  any  further  hesitation  to  reckon  its 
chances  directly. 
^  §  43.  We  may  notice  in  passing  that,  if  we  had  to  suppose 
that  the  series  might  arise  from  some  other  cause,  beside  the 
one  we  have  already  mentioned,  a  further  complication  would 
be  at  once  introduced.  But  this  we  need  not  consider ;  for  the 
most  simple  case  of  inverse  or  inductive  probable  reasoning 
proceeds  as  above,  and  is  sufficient  to  show  the  principle 
employed.  And  we  may  notice  again  that  there  are  assump- 
tions involved,  which  we  shall  have  to  discuss  in  a  following 


Chap.  Vn.]  THE  MODALITY   OF  JUDGMENTS.  20/ 

section.  We  may  here  remark  that,  if  we  are  not  satisfied 
with  a  probable  conclusion,  if  we  go  on  to  assert  that  the  series 
has  actually  been  produced  by  a  cause  of  a  certain  character, 
which  will  opei:ate  again  in  the  unknown  throw,  our  assump- 
tion is  doubtful,  if  it  is  not  false.  But,  to  resume,  however  this 
point  may  be  decided  hereafter,  the  nature  of  our  reasoning] 
on  chances  is  the  same  in  inductive  as  it  is  in  deductive! 
probability.  The  chances  of  the  new  throw  represent  the  pro- 
portion of  our  grounds  for  belief  The  fact  that  these  grounds 
have  been  supplied  by  a  series,  and  the  reduction  of  that 
series  to  its  actual  or  probable  cause,  makes  no  difference  to 
the  principle.  What  grounds  have  we  got  for  determining  the 
throw  that  is  to  take  place  .?  Those  grounds  which  as  causes 
have  determined  the  known  series.  What  are  those  grounds  ? 
They  are  those  from  which  we  go  to  the  series  in  hypothetical 
judgments.  What  is  the  nature  of  these  ?  We  do  not  know 
them  exactly,  but,  so  far  as  known,  we  can  arrange  them  as 
units,  and  groups  of  units,  which  stand  to  one  another  in 
certain  relations.  But  grounds  for  belief,  which  stand  to  one 
another  in  numerical  relations,  are  what  we  mean  by  the 
chances  of  the  throw. 

§  44.  From  this  hurried  account  of  the  general  nature  of 
what  has  been  called  the  Logic  of  Chance,  we  pass  to  the 
removal  of  erroneous  ideas.  It  is  evident,  in  the  first  place, 
J|/that  probability  does  not  affirm  about  the  fact  as  such.  Tb^ 
^ent  rgn^r  hft  pn^t  nnd  absolutely  fixed,  but  our  alternatives 
continue  to  be  truly  asserted.  But,  on  the  other  hand,  if  the 
chances  are  not  facts,  are  they  nothing  at  all  but  our  belief 
about  facts  ?  Is  probability  simply  the  quantity  of  the  belief 
we  happen  to  possess  ?  No,  that  once  more  would  be  in- 
correct. We  need  not  trouble  ourselves  to  discuss  the 
meaning  assignable  to  "  quantity  of  belief,"  for  the  whole  idea 
must  be  banished  at  once.  The  amount  of  our  belief  is 
psychological,  the  probability  of  a  fact  is  always  logical.  No 
matter  what  it  is  we  happen  to  believe  in,  whether  it  exist  or  do 
not  exist,  our  belief  itself  is  unaffected.  But  an  assertion  about 
chances  must  be  true  or  false.  It  depends  on  fact  and  refers 
to  that,  though  it  is  not  true  or  false  of  the  special  fact  in 
question. 


208  THE  PRINCIPLES  OF  LOGIC.  [Book  I.    \ 

§  45.  We  have  not  contradicted  ourselves.  Probability^  ' 
tells  us  what  we  otight  to  believe,  what  we  ought  to  believe  ony^. 
certain  data.  These  data  are  assertions  about  reality,  and  the  \ 
conclusion  as  to  what  we  ought  to  believe  results  from  a  j 
comparison  of  our  grounds  for  belief  Since  these  grounds  are  \ 
the  conditions  of  hypothetical  judgments,  the  judgments  again  \ 
must  be  true  or  false,  and  they  rest  upon  categorical  bases.  1 
In  these  two  points,  (i)  the  general  ground  of  the  disj  unction,  jf- 
and  (ii)  the  special  grounds  of  the  alternatives,  probability  is 
true  or  false  of  reality.     We  may  call  it  "  objective."  \ 

On  the  other  hand  probability  is  "subjective."  If  I  say  ] 
"  The  probability  of  S-P  is  -^V,"  this  may  be  true  although  \ 
S-P  is  impossible.  It  is  true  to-day,  and  to-morrow  it  is  true  \ 
that  the  chance  is ' -^,  and  the  next  day  \.  The  belief  must  ] 
change  with  my  varying  information,  and  it  is  true  through-  ; 
out  these  variations,  and  is  true  though  every  one  of  them  is  \ 
an  error.  How  can  this  be  "  objective  "  ?  It  ^eems  to  lack  \ 
the  very  differentia  of  truth.  1 

[  The  solution  is  obvious.  Within  the  probability  what  is  \ 
i  ftrue  or  false  is  not  the  premises  but  the  conclusion  I  draw  from  J 
i  Hhem.  Given  certain  assumptions,  there  is  only  one  way  of  ; 
stating  the  chances.  Given  certain  grounds  for  belief  or  dis-  : 
belief,  there  is  only  one  correct  inference  to  the  fractional  ; 
result.  This  result  is  neither  "  subjective  "  nor  "  relative,"  ; 
if  those  phrases  mean  that  it  might  be  different  with  different  \ 
men.  From  certain  data  there  is  but  one  conclusion,  and,  i 
if  this  is  different  in  different  heads,  then  one  or  both  of  these  j 
heads  is  mistaken.  Probability  is  no  more  "  relative  "  and  \ 
"subjective"  than  is  any  other  act  of  logical  inference  from  \ 
hypothetical  premises.  It  is  relative  to  the  data  with  which  ; 
it  has  to  deal,  and  is  not  relative  in  any  other  sense.  It  starts  j 
with  certain  assumptions  about  the  nature  of  the  fact,  and  it  j 
tells  us  what,  if  we  are  ready  to  take  these  assumptions  as  \ 
true,  we  ought  to  believe  in  consequence.  If  this  is  not  to  be  \ 
"  objective "  and  necessary,  then  farewell  for  ever  to  both  \ 
these  phrases.  j 

Probability  as  such  is  not  true  of  the  fact,  but  it  always  has  \ 
a  reference  to  fact.  It  is  concerned  with  certain  special  \ 
deductions  from  the  basis  of  propositions  which  are  true  or   \ 


/ 


Chap.   VIL]  THE   MODALITY   OF  JUDGMENTS.  209 

false  in  fact.  It  certainly  is  confined  to  those  deductions. 
But  it  possesses,  when  kept  within  its  own  limits,  truth 
absolute  and  unquestionable  and  that  never  can  vary. 

§  46.  Probability  is  neither  simply  "  subjective  "  nor  yet 
simply  "objective."  This  vicious  alternative  is  the  first  of 
the  errors  we  have  to  dismiss.  It  is  allied  to  another  elemen- 
tary mistake,  which  must  next  engage  us. 

It  is  mere  misunderstanding  which  supposes  that  chance 
involves  a  series,  and  that  the  logic  of  probability  is  essentially 
concerned  with  statistical  frequency.  It  is  mere  error  which 
finds  the  necessary  meaning  of  "  The  probability  of  S-P  is  ^," 
in  "  Once  in  a  series  of  four  events  S-P  will  be  true."  This 
mistaken  theory  contains  some  truth,  but  has  taken  one  part 
of  the  truth  for  the  whole. 

§  47.  Is  the  series  real  or  is  it  imaginary  ?  Let  us  first  take 
it  as  real,  as  something  that  exists,  has  existed,  or  will  exist. 
Must  the  judgment  "  The  chance  of  S-P  is  ^,"  refer  always  and 
essentially  to  an  actual  series  ?  The  assertion  would  be  pre- 
posterous. The  event  S-P  may  be  hypothetical.  It  may 
have  a  probability  of  i  on  the  ground  of  assumptions  which 
we  know  are  not  true.  Where  is  then  the  real  series  ?  The 
event  again  may  be  unique.  The  chance  of  my  dying  before 
I  am  forty  is,  say,  ^  Does  this  mean  that  if  I  die  three  times, 
one  case  will  realize  the  possibility  ?  The  event  once  more 
need  not  be  an  event.  It  need  be  nothing  which  ever  could 
happen  in  time,  and  we  should  deceive  ourselves  if  we  gave 
it  that  name.  "  It  is  even  chances  that  the  soul  is  nothing  but 
a  function  of  the  body  :  "  the  probability  is  ^.  "  It  is  one  to  two 
that  God  is  a  person  :  "  the  probability  is  l.  "  It  is  one  to  ninety- 
nine  that  the  will  is  free  :  "  the  probability  is  tw-*  It  may  be 
said,  no  doubt,  that  the  figures  are  illusory,  and  that  we  can  not 
find  any  unit  of  value  ;  but  I  hardly  think  this  objection  can 
stand.  Admit  that  the  case  is  highly  improbable,  it  still  is 
possible  that  in  the  mind  of  some  man  the  grounds,  present 
for  and  against  such  judgments  as  these,  might  be  reduced  to 
a  common  denominator.  How  can  we  deny  it  ?  and,  if  we  do 
not  deny  it,  what  becomes  of  our  series  ? 

*  Of  course  I  do  not  mean  these  fractions  as  an  expression  of  my 
opinion, 

P 


210  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

X 

§  48.  The  series  clearly  can  not  be  real.  Let  us  take  it  as 
imaginary.  The  question  is  then,  Is  such  a  fictitious  imagi- 
nary series  the  proper  way  in  which  to  represent  probability  ? 
Can  we  say,  It  is  my  meaning,  or  the  only  true  way  in  which 
to  render  my  meaning  ?  This,  I  think,  would  be  an  absurdity. 
It  will  not  stand  a  serious  examination. 

Probability  can  indeed  be  always  represented  by  a  fictitious 
series.  "  It  is  two  to  one  he  is  guilty  "  may  be  rendered  by 
saying,  "  Two  times  out  of  three  a  verdict  on  such  evidence  as 
this  would  be  right."  Even  when  the  possibility  is  unique,  we 
yet  can  abstract  from  that  quality  and  say,  "  Men  such  as  I  am 
would  die  before  forty  two  times  out  of  three.  Nay,  even 
when  we  leave  events  altogether  behind  us,  we  still  can  keep 
up  this  mode  of  expression  by  a  fictitious  series.  Imaginary 
judgments  here  become  the  events.  "  It  is  even  chances  the 
soul  is  a  bodily  function  "  may  be  translated  by  "  In  making 
such  judgments  as  this  a  man  would  be  wrong  through  one 
half  of  the  series  and  right  through  the  other  half" 

But  is  such  a  way  of  putting  our  meaning  the  real  and 
essential  idea  we  entertain  ?  When  we  wish  to  be  correct,  are 
we  forced  so  to  speak  1  It  always  is  possible,  but  is  it  always 
necessary  ?  Is  it  always  even  natural  ?  And  then  there 
remains  a  question  in  reserve.  Is  it  not  incorrect  ? 

§  49.  Let  us  begin  with  its  possibility.  Why  can  we 
always  express  the  chances  by  making  use  of  a  fictitious 
series  }  For  this  reason.  When  the  grounds  from  which  we 
reckon  are  considered  as  causes,  we  are  accustomed  to  suppose 
that  their  issue  in  a  series  of  phenomena  will  exhibit  the  same 
numerical  proportions  that  our  fractions  possess.  If  so,  then 
on  one  side  the  causes  (or  cause)  of  the  series  and,  on  the 
other  side,  the  series  itself  will  answer  to  each  other.  We  say 
what  we  have  to  say  of  the  cause,  indifferently,  either  by 
stating  its  effects,  or  by  setting  out  the  reasons  it  gives  us  to 
expect  one  effect  and  not  another.  This  is  natural  enough 
where  the  fictitious  series  is  imagined  to  be  real.  It  is  not  so 
natural  with  unique  events,  where  the  series  strikes  us  as 
specially  manufactured  to  express  the  chance.  It  is  still  less 
natural  where  the  possibility  itself  is  not  an  event,  and  the 
series  is  nothing  but  the  series  of  judgments.      But  even  here 


Chap.    VII.]  THE   MODALITY   OF  JUDGMENTS.  211 

it  Still  is  possible.  Since  psychologically  the  grounds  are  causes 
(p.  494),  since,  in  other  words,  the  logical  reasons  which  necessi- 
tate the  result  are  what  produces  the  fact  of  the  judgment,  I 
can  imagine,  if  I  please,  a  series  of  judgments,  and  say,  Since 
these  numerically  answer  to  the  reasons  I  have,  therefore 
such  a  numerical  part  will  be  true.  The  expression  by  a 
series  is  here  quite  unnatural,  but  it  still  is  possible. 

§  50.  The  issuing  of  a  certain  series  is  only  one  way  of 
putting  probability.  It  is  sometimes  a  natural  way ;  it  is 
sometimes  a  not  unnatural  way  ;  it  is  sometimes  most  un- 
natural. But  it  is  never  the  right  way  ;  it  is  never  more  than 
a  manner  of  statement  ;  it  is  never  the  real  meaning  and 
intent.  Even  when  I  start  from  an  actual  series,  I  must  leave 
it  before  I  can  get  to  probability.  I  must  go  to  its  cause  by 
what  is  called  a  method  of  reduction,  by  an  inductive  hypo- 
thesis. And  I  can  not  simply  define  this  cause  as  that  which 
either  has  issued,  or  will  issue,  in  a  certain  series.  I  can  not 
do  the  first,  for  that  would  be  certainty  and  not  probability. 
And  I  can  not  do  the  second  without  an  assumption  which  I 
am  unable  to  justify. 

It  is  obvious,  in  the  first  place,  that  to  take  a  series,  and 
to  say  "  The  cause  which  has  produced  this  series — has  pro- 
duced this  series  "  is  merelyJJweletrs.^^On  the  other  hand,  if  I 
add  "  will  produce  this  very  same  series  on  other  occasions,"  that 
is  not  frivolous,  but  is  either  irrelevant  or  else  unjustifiable.  If  it 
means  "  In  another  case  where  the  conditions  are  not  disparate, 
the  same  cause  will  be  followed  by  the  same  effect,"  that 
assertion  is  true  but  is  quite  irrelevant,  because  merely  hypo- 
thetical. For  in  an  actual  fresh  case  I  do  not  know  the  fresh  con- 
ditions, and,  if  I  did,  I  do  not  know  what  the  old  cause  specially 
is.  I  da  not  know  the  actual  cause  (or  causes)  of  the  former 
series.  I  do  not  know  that  these  are  present  again  in  the 
unknown  case.  I  do  not  know  what  conditions  the  fresh  case 
brings  ;  and,  if  I  did,  I  might  be  unable  to  deduce  the  result 
from  the  complication  of  elements.  In  short  I  can  not  go  from 
a  given  series  to  an  unknown  series  or  an  unknown  case.  To 
reason  directly  is  of  course  impossible,  and  I  can  not  reason 
indirectly  through  the  cause,  because  I  do  not  know  the  actual 
cause  in  one  case  or  the  other.     Its  general  character,  to  a 

P  2 


212  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

certain  limit,  I  do  know  in  one  case,  and  assume  in  the  other, 
but  this  general  character  does  not  imply  a  series,  and  the 
individual  cause  itself  I  do  not  know  and  so  can  not  use. 

The  upshot  of  this  is  that  within  probability  you  really  have 
not  got  the  effects  on  one  side  and  the  cause  on  the  other.  If 
then  you  give  as  the  essence  of  probability  the  production  of  a 
series  with  certain  marks,  you  go  beyond  what  your  data 
will  warrant.  For  your  actual  series  has  now  ceased  to  be 
taken  as  a  series  of  events  produced  in  time.  It  has  degene- 
rated into  a  set  of  conflicting  reasons,  possibilities  as  to  an  event 
of  a  certain  sort,  which  in  default  of  detailed  information  I  use 
in  order  to  determine  my  judgment.  My  probabilities  do  not 
represent  a  series  as  such.  I  now  have  nothing  whatever  but 
conflicting  grounds  for  belief  and  expectation,  grounds  for 
belief  as  to  any  fresh  case  or  number  of  cases  that  have  the 
general  character  of  my  series.  And  these  fractional  reasons, 
which  are  all  I  can  work  with,  are  the  same  in  any  one  new 
instance  as  in  any  number  of  new  instances.  Thus  the  sup- 
posed differentia  of  an  imagined  series,  in  the  first  place,  would 
add  nothing  to  the  probability  which  already  exists  apart 
from  the  idea  of  any  series.  But,  in  the  second  place,  if  it 
does  add,  and  if  it  goes  on  to  say  that  the  series  must  have  a 
character  answering  to  the  expectation,  then  it  adds  what  is 
false. 

§  51.  And  with  this  we  come  to  an  obstinate  illusion. 
There  is  a  common  idea  that,  if  you  know  the  chances  of  any 
set  of  events,  you  really  know  the  character  of  the  actual  events 
which  are  to  take  place.  It  is  supposed  that  the  series  will 
correspond  to  the  fractions.  For  instance,  if  we  take  the  case 
of  a  die,  the  chance  of  any  one  face  is  7,  and  from  this  we 
argue,  "  In  a  series  of  throws  each  face  will  be  seen  in  one-sixth 
of  the  run."  But  we  have  no  right  to  any  such  assertion. 
Not  knowing  the  cause,  knowing  only  a  part  while  part  is 
hidden,  we  can  say  no  more  than  that  our  information  leads 
us  to  expect  a  certain  result.  It  is  monstrous  to  argue  that 
therefore  that  certain  result  must  happen.  It  is  false  reason- 
ing a  priori,  and  a  posteriori  the  facts  confute  it.  It  is  not 
found  in  experiment  that  actual  runs  do  always,  or  often, 
correspond  exactly  to   the  fractions  of  the   chances.      That 


Chap.   VIL]  THE  MODALITY  OF  JUDGMENTS.  213 

correspondence  is  after  all  the  most  probable  event,  but  to 
make  it  more  is  a  fundamental  error. 

§  52.  I  shall  return  to  the  truth  contained  in  this  error, 
but  at  present  we  must  try  to  get  rid,  if  we  can,  of  the  error 
itself  We  may  expect  an  objection.  "Experiment,"  it  will 
be  said,  "  does  not  disprove  the  assertion  that  is  made.  That 
assertion  is  not  that  in  a  finite  series  the  numbers  will  come 
right.  They  will  come  right  only  if  we  go  on  long  enough, 
and  in  the  long  run."  But  what  is  this  "  long  run  "  t  It  is 
an  ambiguity  or  else  a  fiction.  Does  it  mean  a  finite  time  } 
Then  the  assertion  is  false.  Does  it  mean  a  time  which  has 
no  end,  an  infinite  time  t  Then  the  assertion  is  7ioiisense.  An_ 
infinite  series  is  of  course  not  possible.  It  is  sel£:i:ontfa:dic- 
tory  ;  it  could  not  bereal.  And^  to  sayilhat  somediiDg  wgll 
ceftaint)rlTappeirunder  impossible_condidons,JsJkr_removed 
from~asserting^tEsl^lity.  The  aflfirmation  that  an  event  may 
be  assumed  to  take  place  in  an  infinite  series,  and  not  outside 
it,  would,  in  the  mouth  of  any  one  who  knew  what  he  meant, 
be  a  suggestion  that  the  event  may  not  take  place  at  all. 

§  53.  I  hope  I  need  not  protest  that  I  am  hardly  so 
foolish  as  to  attempt  to  offer  an  ignorant  objection  to  the  use 
of  infinities  and  infinitesimals  within  the  sphere  of  mathe- 
matics. I  would  rather  say  nothing  at  all  on  this  matter  than 
appear  as  presuming  to  doubt  the  validity  of  processes  em- 
ployed by  the  greatest  men  in  the  exactest  of  sciences.  But 
T  shall  not  so  be  misunderstood.  An  objection  to  the  use 
jwithin  certain  sciences  of  certain  ideas  must  be  taken  within  the 
limits  of  those  sciences.  But  the  use  of  these  ideas  outside  their 
science  carries  with  it  no  authority,  and,  so  long  as  the  general 
meaning  is  understood,  may  be  criticized  by  men  who  are  igno- 
rant of  the  science  in  which  the  ideas  give  brilliant  results.  It  is 
so  with  infinity.  Outside  mathematics  an  infinite  number  is 
an  idea  that  attempts  to  solder  elements  which  are  absolutely 
discrepant.  It  could  not  exist  until  the  world,  as  known 
in  our  experience,  was  utterly  shattered  and  transmuted 
from  the  roots.  I  could  not  find  an  illustration  I  would 
sooner  use  to  express  impossibility.  And  it  is  this  idea  which, 
outside  mathematics,  is  presented  to  us  in  the  error  we  are 
combating.     Mr.  Venn,  for  whose  powers  I  feel  great  respect, 


214  THE   PRINCIPLES   OF   LOGIC.  [Book  I. 

and  from  whose  Logic  of  Chance  we  all  can  learn,  holds  that 
in  the  long  run  every  chance  will  be  realized.  This  "  long 
run,"  he  tells  us,  is  an  infinite  series  (p.  146),  and  (unless  I 
very  much  misunderstand  him)  he  goes  on  to  call  it  a  "  phy- 
sical fact  "  (p.  163).  His  book  is  much  injured  by  this  terrible 
piece  of  bad  metaphysics.  He  has  translated  a  mathematical 
idea  into  a  world  where  it  becomes  an  absurdity. 

§  54.  We  must  everywhere  protest  against  the  introduc- 
tion of  such  fictions  into  logic,  and  protest  especially  where 
the  ideas  are  not  offered  in  the  shape  of  fictions.  The  formula 
of  the  "  long  run "  must  be  banished  from  logic,  and  must 
carry  with  it  a  kindred  illusion  in  the  imbecile  phrase,  "  if 
you  go  on  long  enough."  "  The  event,"  we  are  told,  "  will 
answer  to  the  chances."  But  it  does  not  answer.  "Oh  it 
will,  if  you  only  will  go  on  long  enough.  You  toss  a  coin 
and,  the  chances  being  equal,  if  you  only  go  on  long  enough, 
the  number  of  heads  and  tails  will  be  the  same."  But  this  is 
ridiculous,  r-lf  I  toss  the  coin  until  the  numbers  are  equal,  of 
course  they  will  be  equal.  If  I  toss  it  once  more  then,  by  the 
hypothesis,  they  become  ^meqtial  I  might  just  as  well  say, 
"  If  I  only  go  on  long  enough  the  events  will  certainly  not 
answer  to  the  chances."  Your  formula  is  false  or  else  tauto- 
logous.  If  it  means  "  Suppose  the  numbers  are  equal,  and  sup- 
pose I  then  stop,  the  numbers  will  be  equal,"  that  is  surely  tauto- 
logous.4^  But  if  it  means  the  numbers  will  turn  out  equal  in  an 
infinite  series,  then  that  is  false,  for  such  a  series  is  impossible.* 

§  55.  But  let  us  turn  from  the  error  and  see  the  truth 
which  lies  hid  beneath  it.-f  It  is  false  that  the  chances  must 
be  realized  in  a  series.  It  is  however  true  that  they  most 
probably  will  be,  and  true  again  that  this  probability  is  in- 
creased, the  greater  the  length  we  give  to  our  series.  What 
reason  have  we  for  holding  these  two  beliefs  ?  (i)  Why  do  we 
think  that  the  series  will  probably  answer  to  the  fractions  ? 
(ii)  Why  do  we  think  that  in  a  longer  series  the  correspon- 
dence is  more  likely? 

*  Cf.  Lotze,  Logik^  437.  I  may  remark  that  if  the  formula  meant, 
"  The  series  is  sure  to  cross  and  re-cross  the  point  of  equality,"  then,  in 
the  first  place  it  would  hQ  false,  since  there  is  no  certainty j  and,  in  the 
second  place,  such  an  oscillation  is  not  equality. 


Chap.   VII.]  THE   MODALITY   OF  JUDGMENTS.  21 5 

(i)  Probability,  we  have  seen,  is  not  essentially  concerned 
with  any  series.  4»  It  is  based  upon  grounds  which,  even  if  we 
consider  them  as  real,  may  not  be  causal  in  the  sense  of  pro- 
ductive of  events  in  time.  They  may  be  cmtsce  cognoscendi 
and  not  essendi.^  It  is  when  our  grounds  are  grounds  for 
belief  as  to  the  nature  of  an  agency,  which  is  to  produce  events 
in  time,  that  we  are  able  to  consider  them  as  causal  elements. 
And  this  is  the  case  we  have  to  suppose. 

We  know  that  a  series  is  to  be  thrown  with  a  single  die. 
Let  us  first  take  one  throw.  That  will  have  a  cause,  and  the 
cause  is  only  partially  known.  We  know  that  it  is  complex 
and  consists  of  many  elements.  Of  these  elements,  so  far  as 
they  are  distinctly  known,  five  parts  are  hostile  to  any  single 
face  and  but  one  part  favourable.  The  unknown  residue, 
so  far  as  it  determines  the  case,  is  quite  unknown ;  and, 
though  it  is  not  indifferent  and  though  it  can  not  be  so,  yet 
within  our  knowledge  we  must  take  it  as  indifferent.  In  the 
cause  of  the  single  throw  there  are  therefore,  beside  the  unknown 
factors,  one  sixth  part  of  the  agencies  favourable  to  each  face. 

Now  take  the  whole  series.  That  series,  before  I  throw  it, 
is  as  certain  and  fixed  as  though  I  had  thrown  it  already. 
But  here  again  I  do  not  know  the  causes.  About  one  part  I 
know  nothing  in  detail,  and  so  I  must  take  it  as  being  in- 
different, although  I  am  sure  it  is  not  so  in  reality.  Of  the 
rest  of  the  agencies,  which  I  suppose,  one  sixth  is  favourable 
to  each  face,  and  five  sixths  hostile.  What  conclusion  can  I 
draw  as  to  the  nature  of  the  series  t  Will  one  agency  pro- 
duce that  result  which  we  suppose  it  would  produce,  did  the 
others  not  intervene?  Will  in  each  case  of  the  series  the 
supposed  majority  of  agents  prevail  }  We  have  no  means 
of  knowing.  The  series,  absolutely  fixed,  is  fixed  by  what 
we  do  not  comprehend.  We  must  take  the  possibilities, 
and  the  possibility  for  which  there  is  most  ground  is  the  like- 
liest. There  is  less  ground  to  think  that  in  a  series  of  six 
throws  one  face  will  be  absent,  and  one  twice  present,  than 
that  all  should  show  once.  In  the  latter  case  we  do  but  make 
ignorance  a  ground  for  complete  indifference.  In  the  former 
case  we  give  a  preference  without  any  kind  of  warrant.  It  is 
not  that  each  face  has  any  sort  of  claim  to  come  uppermost 


2l6  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

once.  It  is  that  no  face  has  more  claim  than  another  to  show 
itself  twice.  This  is  why  we  think  the  most  likely  series,  or 
the  least  unlikely,  will  be  that  which  corresponds  to  our 
fractions. 

§  56.  (ii)  But  why,  it  may  be  asked,  does  the  length  of 
the  series  increase  this  probability  ?  Does  the  greater  length 
add  any  new  ground  to  those  we  have  for  believing  in  the 
correspondence  of  the  events  with  the  chances  }  No,  it  does 
not  add  any.  Does  it  decrease  any  ground  we  had  before  for 
thinking  the  opposite  ?  Yes,  it  does  do  that ;  and  it  does  it,  I 
think,  in  the  following  way.  The  unknown  residuum  in  the  cause 
of  each  throw  was  assumed  to  be  indifferent.  But  it  was  not  at 
all  assumed  to  be  passive.  It  supplies  the  determining  element 
in  the  cause.  It  decides  for  one  face,  though  we  do  not  know 
for  which  face  it  decides.  Now  how  does  it  decide  ?  Does  it 
act  quite  regularly  and  in  strict  rotation,  or  is  it  irregular } 
That  we  do  not  know  ;  but,  taking  the  possibilities,  we  believe 
that  those  in  favour  of  irregularity  are  more  than  those  in 
favour  of  rotation.  It  is  therefore  most  probable  that  our 
series  will  turn  out  to  be  irregular.  But,  since  we  know  no 
reason  to  prefer  any  one  face,  we  can  not  say  that  any  pro- 
portion other  than  strict  equality  is  the  most  probable.  How 
are  these  assertions  to  be  reconciled .?  Very  easily  in  this 
way.  Owing  to  the  assumed  indifference  of  the  causal  residue 
the  faces  will  probably  appear  in  their  right  numbers  ;  but, 
because  of  its  irregularity ,  their  appearance  will  probably  be 
irregular,  and  irregular  to  an  extent  to  which  we  can  assign 
no  limit.  To  combine  these  attributes  it  is  necessary  to 
suppose  that  the  whole  series  will  be  most  probably  regular, 
but  will  contain  periodic  irregularities.  The  greater  the 
irregularity  becomes,  the  less  grows  the  chance  of  a  final  regu- 
larity, unless  the  series  is  proportionately  lengthened.  There- 
fore, since  we  can  fix  no  limit  to  the  irregular  sequence  of  the 
faces,  we  conclude  that,  the  longer  the  series  becomes,  the 
greater  becomes  the  probability  of  a  regular  result.  And  this  is 
a  rational,  and  necessary  conclusion  from  our  imperfect  data. 

§  57.  It  is  true  that,  if  you  make  a  series  longer,  you  de- 
crease the  chance  of  irregularity.  It  is  true  that,  if  per 
impossibile  the  series  were  so  long  that,  in  comparison  with 


Chap.  VII.l  THE   MODALITY  OF  JUDGMENTS.  21/ 

its  length,  every  possible  abnormal  run  was  a  period  which 
other  periods  might  easily  balance  in  the  completed  cycle — if, 
I  S2iy,per  impossibile  this  phantom  could  be  real — it  is  true 
that  the  above  chance  of  irregularity  would  vanish.  If  we  as- 
sume that  what  we  do  know  gives  us  reason  to  believe  in  a  series 
correspondent  to  our  fractions  ;  if  we  next  assume,  by  virtue 
of  a  fiction,  that  the  unknown  residue  gives  no  reason  to  be- 
lieve in  an  unbalanced  irregularity,  then  on  these  assumptions 
we  may  go  to  a  conclusion,  and  we  have  no  ground  to  disbelieve 
the  statement  that  the  series  will  exhibit  the  relations  of  the 
chances.  But  the  first  assumption  is  based  on  ignorance,  and 
the  second  is  based  on  a  known  impossibility.  If  we  mean 
to  speak  about  a  series  of  events  that  could  ever  happen,  we 
can  say  but  this.  It  is  certain  there  will  be  a  series,  each 
throw  of  which  will  give  a  single  face.  It  is  possible  that  in  a 
series  of  any  length  but  one  single  face  should  appear  through- 
out. No  arrangement  is  impossible.  It  is  most  probable 
that  the  events  will  answer  to  the  fractions,  but  against  that  pro- 
bability there  still  remains  another  consideration,  the  chance 
arising  from  the  possible  irregularity  of  one  part  of  the  causal 
elements.  This  fraction  is  diminished  by  each  increase  of  the 
series,  but  it  does  not  disappear  and  it  can  not  disappear. 

§  58.  We  do  not  know  that  in  the  long  run  the  events 
will  correspond  to  the  probabilities.  We  do  not  know  that, 
if  we  go  on  long  enough,  every  chance  will  be  realized.  It  is 
mere  superstition  which  leads  us  to  believe  in  the  reality  of 
the  fiction  which  gives  birth  to  these  chimaeras.  When  I  see 
the  demonstrations,  offered  to  gamblers  against  a  bank,  which 
prove  to  them  that  in  the  long  run  they  can  not  but  lose,  I  say 
to  myself.  On  which  side  do  I  see  the  darker  illusion  }  And  I 
answer,  On  both  sides  the  illusion  is  the  same.  For  what  is 
the  root  of  the  gambler's  "system  "  }  Is  it  not  his  belief  that 
independent  events  are  affected  by  each  other?  But  this 
belief  is  a  strict  deduction  from  the  premises  offered  him.  If 
he  really  must  lose,  if  there  really  is  a  cycle  in  which  the 
chances  must  all  be  realized,  then,  let  him  observe  the  begin- 
ning of  the  cycle,  and  mark  the  irregularities,  and  he  surely 
must  win.  Since  to  equalize  the  numbers  the  end  of  the 
cycle  must  balance  the  beginning,  he  can  speculate  on  that 


2l8  THE   PRINCIPLES   OF   LOGIC.  [Book  L 

balance  and  his  "  system  "  is  right.  "  Oh,  but  it  is  wrong,  for  the 
series  is  not  finite.  It  is  only  after  an  infinite  duration  of  play 
that  the  balance  is  struck.  It  is  absurd  to  say  he  can  be  sure 
of  winning."  But  is  it  not  then  equally  absurd  to  say  that  he 
is  sure  to  lose  ?  If  you  mean  he  must  have  lost  by  the  end 
of  his  life,  you  have  just  admitted  your  assertion  to  be  false. 
If  you  mean  he  must  have  lost  when  he  has  got  to  the  end  of 
infinite  time,  confess  that  your  meaning  is  something  like 
nonsense,  and  that  the  gambler  is  right  in  imagining  that 
you,  as  a  rational  man,  must  mean  something  else.  The 
truth  is  that  your  common  assumption  is  false.  There  is  no 
must  about  it.  The  chances  consist  of  grounds  for  belief  in 
the  nature  of  a  series  no  event  of  which  is  known.  And  all 
they  tell  us  is  this  :  that  we  have  more  reason  to  expect  one 
thing  than  we  have  to  expect  another,  and  that  the  increased 
length  of  the  series  proportionately  decreases  a  reason  for 
doubt,  which  never  quite  vanishes. 

§  59.  I  must  not  be  suspected  of  a  desire  to  intrude  into 
mathematics  if,  in  this  connection,  I  venture  to  remark  on  a 
well-known  paradox.  I  am  to  toss  a  coin,  and  to  go  on  toss- 
ing so  long  as  I  throw  heads  and  nothing  but  heads.  I  am  to 
receive  £2  if  I  throw  head  once  ;  if  I  throw  head  twice  I  am 
to  win  £^  ;  for  three  successive  heads  I  get  ;^8,  and  so  on 
accordingly.  The  series  is  supposed  to  have  no  limit  except  the 
appearance  of  a  tail.  And  the  question  arises,  how  much  am 
I  to  pay  for  the  privilege  of  one  single  trial  }  The  answer 
given  is.  An  infinite  sum ;  for  it  is  possible  I  may  throw  an 
infinite  series  of  nothing  but  heads  (vid.  De  Morgan,  Proba- 
bilities, p.  99).  The  reasoning  on  which  this  conclusion  seems  to 
rest  is  exceedingly  simple,  and  I  need  hardly  say  that  I  do  not 
doubt  its  perfect  validity  within  mathematics.  And  I  think 
I  see  that  no  other  answer  can  possibly  be  given.  Unless  an 
arbitrary  limit  is  fixed,  I  may  be  allowed  to  say  in  all 
humility  that  I  think  I  understand  that,  if  this  possibility  has 
any  value  at  all,  then  the  worth  of  my  chance  is  either  incal- 
culable or  else  is  infinite.  If  this  answer  is  given  me  by  a 
special  science,  I  dutifully  receive  it  as  true — within  that 
science. 

But   if  I  am  told  that  in  actual  fact  the  result  is  true,   I 


Chap.   VII.]  THE   MODALITY   OF  JUDGMENTS.  219 

must  be  allowed  to  protest.  I  must  be  permitted  to  remark 
that  the  reasoning  is  absurd  and  the  result  is  nonsense.  I  do 
not  mean  merely  that  it  is  absurd  if  we  take  it  as  a  practical 
precept,  because  a  man  can  not  live  for  ever,  and  all  the 
money  in  the  world  is  finite.  I  mean  that  it  is  a  theoretical 
absurdity.  It  is  not  true  ideally  any  more  than  really.  Since 
an  infinite  sum  is  an  impossibility,  the  infinite  series  can  not 
possibly  be  thrown.  There  is  no  chance  whatever.  There 
is  no  fraction  at  all.  It  is  nothing  I  could  win.  It  is  nothing 
I  can  expect.  It  is  nothing  for  which  I  can  reasonably  pay. 
The  result  is  a  deduction  from  premises  known  to  be  false 
and  impossible. 

It  is  idle  to  answer  that  the  problem  is  "stated  in  the 
ideal  form"  (Venn,  ibid.  p.  137).  There  is  a  difference  surely 
between  ideals  which  as  such  do  not  exist,  because  they  are 
abstractions,  and  ideals  which  are  downright  self-contradic- 
tions. It  is  one  thing  to  say,  "  There  is  a  connection  between 
abstract  elements,  so  that  when  one  of  these  is  found  as  a 
real  quality  we  shall  have  the  other/'  and  another  thing  to 
continue  this  assertion,  when  we  know  that  the  first  of  these 
elements  is  self-contradictory  and  could  not  possibly  be  any 
quality  of  reality.  In  this  latter  case  what  is  true  of  fact  can  not 
be  the  consequence  of  an  impossibility,  but  only  the  basis  of 
the  hypothetical  judgment.  Neither  antecedent  nor  con- 
sequent is  taken  as  real  or  even  as  possible.  But  in  a 
common  abstract  judgment  the  antecedent  is  taken  as  at  least 
a  possible  quality  of  the  world.  Mr.  Venn  perhaps  would 
question  this  difference  between  an  abstraction  and  an  im- 
possibility, and  would  perhaps  assert  that  an  infinite  series  is 
really  possible.  In  any  case  I  must  be  allowed  to  protest 
against  the  invasion  of  logical  reason  by  mathematical  fictions. 
If  an  infinite  series  is  thought  possible,  we  should  be  told  how 
it  can  be  possible.  If  it  is  not  thought  possible,  it  should  not 
be  offered  us  as  if  it  were. 

§  60.  There  are   other  points   in   the   theory   of  chances 

which  have  logical  interest,  but  we  have  no  space  to  discuss 

them  here.     We  have  said  enough  to  make  clear  the  relation 

.in  which  that  theory  stands  to  our  general  principles.      We 

I  have   to   avoid   the  fiction  of  the  infinite  long  run,  and  the 


220  THE  PRINCIPLES  OF  LOGIC.  [Book  L 

vicious  alternative  of  "  objective  "  and  "  subjective,"  and  the 
false  assumption  that  the  essence  of  chance  involves  a  series 
of  events  in  time.  If  we  keep  clear  of  these  pitfalls,  the  truth 
is  by  no  means  difficult  to  reach,  and  we  hope  above  to  have 
stated  it  clearly  in  its  general  form.* 

§  6i.  There  is  an  aspect  of  modality  we  have  neglected 
to  notice.  The  omission  was  intentional,  and  the  mention  of 
this  aspect  has  been  reserved  for  the  present  place.  There  is 
[an  old  doctrine  which  connects  universality  with  necessity, 
and  that  doctrine  is  true.  The  necessary  we  saw  was  the 
ideal  consequent,  and  such  a  consequent  can  not  come  except 
from  an  ideal  antecedent.  You  never  can  say  "  B  follows 
from  A,"  "  is  because  of  A,"  "  must  be,  given  A,"  unless  A  is 
present  in  a  determinate  form.  A  must  be  a  content  without 
any  mixture  of  mere  sensuous  conditions.  It  must  be  ideal, 
abstract,  and  so  universal.  If  the  ancient  doctrine  on  its 
logical  side  may  suffer  some  loss,  since  necessity  becomes  for 
logic  hypothetical,  yet  it  stands  all  the  firmer.  The  "  because  'V 
can  not  couple  anything  but  universals. 

§  62.  We  may  notice  an  error  which  creeps  in  with  this 
truth.  The  antecedent  in  necessity  must  be  universal,  but  it 
need  not  be  more  universal  than  the  consequent.  Where  we 
say  "because"  we  do  not  always  appeal  to  anything  more 
abstractly  general  than  that  which  follows  from  our  reason. 
"  A  must  be  equal  to  B,  because  C  is  equal  to  both  B  and  A," 
"A  must  be  removed  by  one  foot  from  C,  since  B,  which 
touches  both  in  a  certain  manner,  is  one  foot  long."  The 
consequence  is  not  less  general  than  the  antecedent,  and  we 
deceive  ourselves  in  thinking  it  always  must  be  so. 

No  doubt  in  the  cases  where  you  say  "  because  "  you  may 
find  what  we  call  the  principle  of  the  sequence,  and  that  of 
course  must  be  more  abstract  than  the  actual  consequent. 
But  the  principle  is  not  the  antecedent  itself  It  is  the  base 
of  the  general  connection,  not  the  sufficient  reason  of  the 
particular  consequent.      There    is    no    more    need   for    the 

*  The  books  from  which  on  this  subject  I  have  learnt  most  are  Lotze, 
Logikj  Sigwart,  Logikj  Wundt,  Logik;  Jevons,  Principles  of  Science  j 
Venn,  Logic  of  Chance;  De  Morgan,  Probabilities. 


Chap.   VH.]  THE   MODALITY  OF  JUDGMENTS.  221 

consequent  to  be  more  concrete  than  the  antecedent,  than 
there  is  for  the  effect  to  be  more  special  than  the  cause. 
These  ideas  are  nothing  but  kindred  illusions  (Book  III. 
Chap.  II.). 

§  63.  We  shall  have  to  return  hereafter  to  this  point,  but 
have  been  right  to  anticipate  here  the  conclusion.  We  have 
indeed  begun  some  time  back  to  anticipate  the  conclusions  we 
have  to  reach  in  the  following  Books,  since  already  unaware  we 
have  entered  their  territory.  Silently  before  in  the  second 
Chapter,  and  now  almost  explicitly  we  have  made  the 
transition  from  judgment  to  inference.  In  both  the  latter 
kinds  of  modality  we  reason  openly.  iThe  possible  is  that 
which  we  argue  would  follow  from  certain  premises,  part  of 
which  are  taken  as  true.  The  necessary  is  that  which  we 
infer  must  follow,  if  its  grounds  are  premised.  It  was  in 
this  sense  that  possibility  was  one  kind  of  necessity.  In  both 
alike  we  deal  with  conclusions,  reasoned  results  from  given 
data.  In  logic  we  find  that  a  necessary  truth  is  really  an 
inference,  and  an  inference  is  nothing  but  a  necessary  truth. 
This  is  the  secret  which  we  hardly  have  kept,  and  with  the 
discovery  of  which  we  may  pass  at  once  to  our  Second  Book:  f 


BOOK  II. 

INFERENCE. 

At  the  end  of  our  First  Book  we  made  a  transition  to  the 
subject  of  our  Second.  Modality  took  us  from  judgment  to 
reasoning.  An  inference  is  either  a  result  or  a  process.  If 
we  take  it  as  a  result,  we  saw  that  it  is  the  apprehension  of  a 
necessary  truth.  If  we  take  it  as  a  process,  it  is  simply  the 
operation  which  leads  to  that  result.  A  truth  judged  true 
because  of  something  else,  and  the  going  to  a  truth  from 
the  ground  of  a  judgment  or  supposition  are  what  we  mean 
by  conclusion  and  reasoning.  And  this  starting-place  being 
reached,  our  right  course  may  seem  plain.  We  should  first 
make  quite  clear  the  general  character  of  inference,  and 
should  exemplify  this  by  the  necessary  detail.  And  then  we 
might  proceed  at  our  ease  to  remove  the  erroneous  doctrines 
which  cumber  the  ground. 

There  is  an  objection  to  this  way  of  dealing  with  the 
subject.  The  reader  would  find  his  difficulties  increased.  I 
do  not  indeed  know,  after  my  first  Book,  if  at  this  stage  I  have 
any  actual  reader  ;  but  I  am  sure,  if  I  have  one,  that  he  is  not 
eager  to  make  a  great  effort.  We  have  perhaps  nothing  in 
front  of  us  so  hard  to  cross  as  what  we  have  passed  over,  and 
yet  we  shall  find  there  are  obstacles  enough.  It  is  better  to 
make  a  gradual  advance.  Instead  of  going  at  once  from  the 
facts  to  the  truth,  and  from  that  to  the  removal  of  erroneous 
theories,  I  shall  aim  at  reaching  an  easy  vantage-ground,  from 
which  we  may  disperse  the  mass  of  mistakes  which  bar  our 
progress  and  harass  each  movement.  This  will  be  the  object 
we  shall  try  to  gain  first.  Secure  in  our  rear,  we  may  then 
proceed  upon  the  final  position. 


224  THE   PRINCIPLES   OF   LOGIC.  -[Book  II. 

We  must  therefore  in  the  first  of  the  two  following  Books 
be  content  with  a  truth  which  is  only  partial.  We  must 
assume  that  ^n  every  valid  inference  no  less  than  three  terms 
are  given  to  the  reasoner. )  We  shall  hereafter  see  that  this 
assumption  is  not  tenable,  but  it  will  serve  as  a  basis  from, 
which  to  operate.  It  may  be  a  high  thing  to  have  no  order 
of  convenience,  to  follow  the  developement  of  the  subject 
matter,  and  to  let  the  reader  follow  if  he  can.  But  it  is  an 
end  more  possible,  and  perhaps  not  much  lower,  to  help  the 
reader  by  any  means  whatever  to  a  better  understanding. 

The  arrangement  of  this  Book  as  well  as  its  basis  must  be 
considered  arbitrary.  I  shall  begin  by  setting  down  some 
characteristics  of  inference  which  perhaps  are  likely  to  be 
accepted  by  all.  And  to  these  I  shall  add  a  few  examples  of 
actual  reasoning.  I  shall  then  proceed  to  deal  with  some 
mistakes,  confining  myself  in  the  main  to  the  syllogism.  In 
the  next  place  I  will  point  out  that  inference  consists  in  an 
ideal  construction.  And  fourthly  I  will  state  some  principles 
of  synthesis  by  which  we  operate  to  effect  that  construction. 
One  essential  factor  in  valid  inference  will  then  be  indicated, 
and  will  be  seen  to  rest  on  a  serious  assumption  :  and  we  shall 
further  show  that  in  every  inference  at  least  one  premise  must 
be  universal.  Having  reached  this  point  we  shall  conclude  our 
First  Part,  and  take  a  fresh  departure  ;  and  throughout  the 
rest  of  this  Second  Book  we  shall  be  engaged  in  the  work  of 
clearing  the  ground.  We  shall  have  to  criticize  in  general 
the  alleged  Association  of  Ideas,  and  especially  the  Association 
of  Similars.  We  shall  briefly  dispose  of  the  supposed  way  of 
arguing  from  particulars  to  particulars  ;  and  shall  show  by  an 
examination  of  J.  S.  Mill's  Canons  that  his  Inductive  Logic  is 
theoretically  invalid.  After  this,  having  declined  to  enter  on 
a  discussion  of  Mr.  Spencer's  doctrine,  we  shall  end  with  a 
review  of  Professor  Jevons'  theory  of  Equational  Logic.  The 
position  we  shall  have  reached,  and  the  negative  results 
we  shall  have  been  forced  to  gain,  will  have  served  to  prepare 
us  for  a  completer  view. 


(      225       ) 


PART  I. 

THE  GENERAL  NATURE  OF  INFERENCE. 

CHAPTER  I. 

SOME   CHARACTERISTICS   OF   REASONING. 

§  I.  When  we  first  consider  the  subject  of  reasoning  we  seem 
to  have  nothing  but  a  conflict  of  opinion.  But  a  second  glance 
reveals  some  agreement.  There  are  three  characteristic  features 
of  inference  as  to  which  in  our  hearts  we  are  really  at  one.  '  I 
do  not  mean  that  we  should  not  deny  them  if  our  theories  re- 
quired it,  but  we  should  do  so  unwillingly  and  with  a  sense  of 
compulsion.  The  first  of  these  is  a  negative  mark.  There  is  a 
difference  between  reasoning  and  mere  observation  ;  if  a  truth 
is  inferred  it  is  not  simply  seen,  and  a  conclusion  is  never  a 
mere  perception.  The  latter  may  seem  to  be  given  to  us 
bodily,  but  the  former  involves  some  other  element.  It  may 
indeed  be  thrust  upon  us,  we  may  be  compelled  and  con- 
strained to  make  it,  but  we  can  not  passively  take  it  in.  The 
fancies  we  cherish  in  respect  of  perception  desert  us  as  soon 
as  we  come  to  inference.  The  external  fact  or  the  reflection 
it  throws  off  can  violently  break  into  and  enter  our  minds,  or 
the  reality  can  stamp  our  yielding  substance  with  its  image 
and  superscription.  But  we  can  hardly  apply  these  ideas  to 
a  conclusion,  for  we  feel  that  in  this  there  is  something  that 
repels  them.  An  inference  can  not  wholly  come  in  from  with- 
out or  be  passively  received.  It  is  not  mere  vision,  it  is  more 
than  observation. 

§  2.  There  is  another  mark  which  a  conclusion  possesses. 
It  is  not  a  mere  fragment  or  isolated  unit  ;  it  does  not 
exist  in  and  by  itself,  but  is  the  result  of  a  process.  It  rests 
upon    a   basis,    and    that    basis    is    something    we    already 

Q 


226  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  I. 

know.*  In  inference  we  advance  from  truth  possessed  to  a 
further  truth  ;  and  the  conclusion  would  never  be  reached  at  all 
if  it  were  not  for  knowledge  already  attained.  It  is  therefore 
dependent  and  in  a  sense  adjectival. 

§  3.  But  there  is  another  attribute  which  a  conclusion  has^^ 
got.  It  must  convey  some  piece  of  information,  and  must  tell 
us  something  else  than  the  truths  it  depends  upon.  (We  have 
no  inference  at  all,  we  have  simply  a  frivolous  show  and  pretence, 
if  taking  something  we  already  know  we  assert  the  whole  or  part 
of  this  once  more,  and  then  say,  "  I  have  reasoned  and  got  to  a 
conclusion."  An  inference  must  be  more  than  a  vain  repetition, 
and  its  result  is  no  echo  of  senseless  iteration.  It  is  not  mere 
observation  yet  it  gives  us  something  new.  Though  not  self- 
existent  it  is  more  than  a  shadow.  To  those  who  delight  in 
discrepant  metaphors  we  may  bring  conviction  when  we  so 
express  ourselves  :  The  truth  which  is  seen  in  the  mirror  of 
inference  has  not  wandered  in  through  the  window-pane  of 
sense,  nor  yet  is  it  merely  a  reflection  cast  by  an  article  of 
furniture  already  in  the  mind. 

§  4.  Except  in  the  interest  of  a  preconceived  theory,  I 
think  that  these  statements,  at  least  so  far,  will  not  be  denied. 
But  I  can  hardly  hope  that  the  examples  of  reasoning  I  am 
about  to  produce  will  all  escape  unchallenged.  Yet  I  shall 
not  defend  them,  for  I  do  not  know  how.  They  are  palpable 
inferences,  and  the  fact  that  they  are  so  is  much  stronger  than 
any  theory  of  logic. 

(i)  A  is  to  the  right  of  B,  B  is  to  the  right  of  C,  therefore 
A  is  to  the  right  of  C.  (ii)  A  is  due  north  of  B,  B  due  west  of 
C,  therefore  A  is  north-west  of  C.  (iii)  A  is  equal  to  (greater 
or  less  than)  B,  B  is  equal  to  (greater  or  less  than)  C,  therefore 
&c.  (iv)  A  is  in  tune  with  B,  and  B  with  C,  therefore  A  with 
C.  (v)  A  is  prior  to  (after,  simultaneous  with)  B,  B  to  C, 
therefore  A  to  C.  (vi)  Heat  lengthens  the  pendulum,  what 
lengthens  the  pendulum,  makes  it  go  slower,  therefore  heat 
makes  it  go  slower,  (vii)  Charles  I.  was  a  king ;  he  was  be- 
headed, and  so  a  king  may  be  beheaded,  (viii)  Man  is  mortal, 
John  is  man,  therefore  John  is  mortal.  We  shall  go  from  these 
facts  to  ask  how  far  certain  theories  square  with  them. 

'^  For  the  sake  of  clearness  I  here  ignore  the  hypothetical  character 
of  inference. 


(      227      ) 


CHAPTER  11. 

SOME  ERRONEOUS  VIEWS. 

§  I.  The  task  before  us  in  the  present  chapter  is  the 
removal  of  certain  mistaken  ideas.  And  the  first  to  go  must 
be  the  major  premise.  We  saw,  at  the  end  of  the  foregoing 
Book,  that  the  necessary  truth  need  be  no  more  particular 
than  the  truth  it  depends  on,  and  that  logical  necessity  does 
not  alway?  come  from  the  application  of  universals  to  some- 
thing less  universal.  But  if  so,  there  need  not  be  always  a 
major  ;  and  the  examples  we  have  given  put  this  beyond 
doubt. 

In  (viii)  our  old  friend  is  still  to  be  found,  but  in  (vi)  and 
in  (vii)  you  will  hardly  be  able  to  distinguish  him  from  the 
minor,  and  in  all  the  rest  he  has  totally  vanished.  You  may 
say  that  in  (iii)  we  really  argue  from  **  Things  equal  to  the 
same  are  equal  to  each  other,"  and  I  do  not  doubt  you  will 
find  believers.  But  if  such  reasoning  is  reasoning  from  an 
axiom,  how  did  people  reason  before  axioms  were  invented } 
And  if  without  axioms  it  is  impossible  to  infer,  I  wonder 
where  all  the  axioms  can  have  come  from  (cf.  Book  III.  Part 
II.  Chap.  I.).  But  if  we  take  an  example  like  number  (i),  will 
any  one  show  me  the  major  there  ?  "A  body  is  to  the  right 
of  that  which  that,  which  it  is  to  the  right  of,  is  to  the  right 
of.'*  I  know  this  major,  because  I  have  just  manufactured 
it ;  but  you  who  believe  in  major  premises  and  who  scores  of 
times  must  have  made  the  inference,  confess  that  you  never 
saw  this  premise  before. 

We  must  either  admit  that  a  major  is  not  necessary,  or 
else  we  must  say  that  my  examples  are  not  inferences  because 
they  have  no  major.  In  either  case  an  effete  superstition  will 
be  doorned. 

g  2 


228  THE   PRINCIPLES  OF   LOGIC.  [Bk.  XL  Pt.  L 

Begotten  by  an  old  metaphysical  blunder,  nourished  by  a 
senseless  choice  of  examples,  fostered  by  the  stupid  conserva- 
tism of  logicians,  and  protected  by  the  impotence  of  younger 
rivals,  this  chimaera  has  had  a  good  deal  more  than  its  day. 
Really  dead  long  since  I  can  hardly  believe  that  it  stands 
out  for  more  than  decent  burial.  And  decent  burial  has 
not  yet  been  offered  it.  Its  ghost  may  lie  quiet  when  it 
sees  that  the  truth,  which  lent  it  life,  can  flourish  alone  ( cf. 
Book  III.). 

§  2.  The  major  premise,  we  have  seen,  is  a  delusion,  and 
this  augurs  ill  we  may  think  for  the  syllogism.  Our  suspicion 
is  well  founded,  for  the  syllogism  itself,  like  the  major  premise, 
is  a  mere  superstition.  It  is  possible  no  doubt,  as  in  our 
seventh  example,  to  have  a  syllogism  which  has  either  no 
major  premise,  or  at  all  events  no  minor.  And  it  is  unques- 
tionably true  that  in  many  arguments  a  major  premise  is 
actually  used.  Nor  will  I  deny  that  some  three  fourths  of  our 
valid  arguments  can  be  got  within  the  forms  of  Barbara 
Celarmt.  ^  But  yet  after  all  the  syllogism  is  a  chimaera,  for  it 
professes  to  be  the  model  of  reasoning,  and  there  are  reason- 
ings which  can  not  by  any  fair  means  be  conformed  to  its 
pattern.j  In  whatever  sense  you  interpret  it,  it  turns  out 
insufficient ;  and  in  certain  cases  it  will  turn  out  worse.  Let 
us  examine  the  principles  of  reasoning  it  lays  down. 

§  3.(lf  we  take  first  the  axiom  of  inclusion  in  extension  as 
it  finds  expression  in  the  maxim  De  omni  &c.,  we  are  forced  to 
say  that  this  principle  is  unsound.  It  sins  against  the  third 
characteristic  of  inference  (Chap  I.  §  3),  for  it  does  not  really 
give  us  any  new  information.)  And,  as  has  been  long  ago 
remarked,  it  embodies  a  petitio ;  for  if,  asserting  the  premise 
"All  men  are  mortal,"  I  understand  by  the  subject  each 
single  man,  then  I  either  am  aware  that  John  is  mortal,  or  if 
not  my  major  must  be  withdrawn.  The  major  premise  has 
asserted  something  of  each  member  of  a  collection,  and  the 
minor  and  conclusion  do  but  feebly  re-echo  one  part  of  this 
statement.     But  that  is  no  inference. 

We  might  try  to  understand  the  assertion  differently.  We 
might  say  that  what  "  All  men  "  really  means  is  the  collection 
or  class  and  not  each  one  member.     But,  if  so,  we  fall  blindly 


CiiAP.  II.]  SOME  ERRONEOUS   VIEWS.  229 

into  a  second  pitfall.  John's  personality  perhaps  has  no 
unity,  but  he  can  hardly  be  called  a  collection  of  men,  and 
our  syllogism  now  fails  through  quaternio  terminorum.  It 
perhaps  fails  too  through  falsity  of  the  major. 

The  dicUtm  de  onini  thus  turns  out  vicious.  But  if  it  were 
sound  it  would  not  be  sufficient,  for  it  does  not  cover  all  valid 
reasonings. 

§  4.  There  is  another  mode  of  interpreting  the  major. 
"All  men  are  mortal"  may  be  said  to  assert  the  identity  of 
the  subjects  in  "  men"  and  "  some  mortals  ;  "  and  "  John  is  man 
and  therefore  mortal "  assures  us  that  the  subject,  which  we 
distinguish  as  John,  is  identical  with  a  member  of  the  class  of 
men  and  also  of  mortals.  But  we  know  already  how  this  is 
to  be  read.  The  identity  of  the  subject  is  another  way  of 
affirming  the  conjunction  of  diverse  attributes.  The  fact  we 
have  got  is  either  the  co-existence  in  one  single  subject  of  the 
attribute  mortal  with  the  rest  of  John's  attributes,  or  else  the 
possession  by  a  single  thing  of  the  several  names  "John," 
"  man,"  and  "  mortal  "  (cf  Book  I.  Chaps.  I.  and  VI.).  And 
interpreted  in  this  way,  though  the  inference  is  valid,  it  will 
not  fall  under  the  dictum  de  omni. 

§  5.  We  may  illustrate  the  above  from  complete  induction. 
I  may  show  that  all  planets  move  in  an  ellipse  by  counting 
and  observing  each  single  planet.  But  in  what  sense  am  I 
then  said  to  perform  an  inference  ?  I  say  "  therefore  all 
planets  move  in  an  ellipse,"  but  I  know  already  that  every 
single  planet  does  so  move.  If  there  were  any  planet  which  I 
could  not  so  qualify  I  could  not  go  on  to  therefore  all  planets. 
Does  the  "  therefore  "  simply  reiterate  the  "  because,"  then 
there  is  clearly  no  inference.  Does  the  conclusion  assert  that 
the  collection,  or  class,  itself  moves  through  space  in  an 
elliptical  manner  ?  If  this  were  true  the  premises  would  not 
prove  it.  But  perhaps  it  means  that,  if  anything  is  a  known 
planet,  it  must  have  a  course  which  will  be  found  elliptical. 
We  are  free  to  forget  that  the  individuals  we  know  do  move 
in  ellipses.  We  have  firmly  established  a  connection  of 
attributes,  so  that  hereafter,  given  any  single  individual  which 
we  barely  perceive  to  be  a  known  planet,  we  can  go  at  once 
from  the  base  of  that  attribute  to  elliptical  movement,     But 


230  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Ft.  L 

the  conclusion  here  does  not  rest  on  enumeration  complete  or 
otherwise ;  it  proceeds  from  and  rests  upon  a  distinguished 
connection  of  attributes  (Book  I.  Chap.  VI.  and  Bk.  II.  II. 
Chap.  III.  §  3). 

We  may  sum  up  the  matter  thus.  If  you  say  "Each 
individual  has  a  certain  attribute  and  therefore  each  has  it," 
that  is  absurd.  If  you  say  "  therefore  the  collection  has  it," 
that  is  invalid.  If  you  say  "Anything  belonging  to  the 
collection  has  it  and  therefore  this  has  it,"  then  that  is 
valid,  but  the  "  anything  belonging "  stands  for  an  attribute. 
Com  plete  induction  shares  the  fortunes  of  the  syllogism. 

§  6.  The  principle  of  inclusion  within  class  extension  is  not 
merely  insufficient,  but  unless  we  interpret  it  as  a  connection  of 
attributes  it  is  intrinsically  vicious.  Let  us  see  if  we  can  find 
any  other  view  which  will  come  to  the  rescue  and  will  save  the 
syllogism.  "  What  stands,"  says  Kant,  "  under  the  condition  of 
a  rule  stands  under  the  rule."  It  is  thus  he  interprets  "  nota  notce 
estnota  reiipsiusT  If  you  have  an  universal  connection  of  two 
attributes,  then,  given  one  in  a  subject,  you  must  also  have  the 
other. 

It  is  evident  that  this  principle  of  reasoning  is  valid,  but  it 
will  not  cover  the  whole  of  the  ground ;  for,  confined  to  the 
category  of  subject  and  attribute,  it  fails  wherever  you  pass 
beyond.  The  subject  no  doubt  is  in  some  way  qualified  by 
whatever  can  be  asserted  about  any  of  its  attributes,  but  it  is 
idle  to  expect  a  result  from  this  where  we  are  not  concerned 
with  Subject  and  attributes.  "A is  prior  to  B  andB  to  C,  and 
therefore  A  is  prior  to  C,"  but  what  here  am  I  to  call  the 
"  condition  of  the  rule  "  or  the  "  nota  "  or  "  attribute  "  ?  I  can 
not  take  B  as  the  attribute  of  A,  and  if  I  look  for  that 
attribute  in  "prior  to  B,"  I  fall  at  once  into  quaternio 
terminoruniy  since  the  second  premise  has  got  B  simply. 

And  even  when  we  keep  to  subjects  and  qualities,  there 
are  inferences  which  the  principle  will  not  justify.  The 
syllogistic  third  figure  can  hardly  be  supposed  to  exemplify 
the  axiom  which  Kant  has  adopted.  Not  only  is  the  category 
of  subject  and  attribute  (as  commonly  applied)  unable  to  cover 
the  whole  field  of  reasoning,  but  within  that  category  it  is  a 
further  mistake  to  insist  on  the  necessity  of  a  major  premise. 


Chap.  II.]  SOME  ERRONEOUS   VIEWS.  23 1 

§  7.  It  is  evident  that  the  syllogism  can  not  be  saved  or 
can  only  be  saved  in  such  a  way  as  to  be  syllogism  no  longer. 
The  one  chance  there  is  of  preserving  the  syllogism  is  for  us 
to  take  our  stand  upon  the  third  figure.  "  The  attributes  of 
one  subject  are  interrelated  "  will  then  become  the  axiom  of 
inference.  We  have  seen  ( §  4)  that  all  syllogisms  in  extension 
can  be  interpreted  according  to  this  axiom,  since  the  identity 
of  the  subject  was  the  other  side  of  that  relation  of  attributes 
which  we  wished  to  assert.  And  it  is  evident  again  that  all 
relations  of  attributes  can  be  regarded  as  based  in  a  subject. 
We  shall  see  hereafter  (Part  II.  Chap.  IV.)  that  Substitution 
of  Similars  can  be  taken  as  syllogism  within  the  third  figure  ; 
and  I  will  go  yet  further.  There  is  and  there  can  be  no  in- 
ference whatever  which  may  not  be  reduced  under  the  head  of 
the  axiom,  since  everything  which  in  any  way  is  conjoined 
can  be  taken  as  related  within  some  subject  (Book  III.  Chap. 

VI.  §§33,  34)- 

We  may  see  hereafter  how  this  reduction  is  effected. 
For  our  present  purpose  it  is  enough  to  remark  that  in  many 
cases  it  can  not  be  performed  without  processes  which  would 
horrify  the  conservative  logician,  and  which  gain  no  end  worth 
the  violence  they  use.  Unless  "subject  and  attribute"  are 
used  in  a  way  which  is  quite  unknown  to  the  traditional  logic, 
the  axiom  fails  of  universal  validity,  for  it  does  not  apply  to 
any  of  those  relations  which  two  or  more  subjects  bear  to  each 
other.  "  Two  pianos  are  in  tune  with  one  fork  and  therefore 
the  one  is  in  tune  with  the  other."  But  in  this  instance,  unless 
the  terms  are  manipulated  freely,  you  will  not  show  one 
subject  with  its  attributes. 

§  8.  It  is  obvious,  if  we  fairly  consider  the  examples  which 
have  been  adduced  at  the  end  of  Chapter  I.,  that  the  syllogism, 
if  it  keep  its  traditional  form,  is  in  great  part  impotent.  And 
I  confess  I  do  not  know  what  policy  will  seem  good  to  the  friends 
of  the  syllogism.  They  may  boldly  accept  the  violent  alterna- 
tive of  excluding  all  examples  which  they  can  not  deal  with. 
But  I  think  we  may  say  that  such  a  course  as  this  would  be 
nothing  short  of  a  confession  of  bankruptcy.  If  a  savage  may 
know  the  road  that  will  take  him  from  A  to  B,  and  the  road  that 
will  take  him  from  B  to  C,  and  yet  may  not  know,  and  may 


232  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  I. 

be  unable  to  find  out,  the  way  he  should  go  from  A  to  C  (cf. 
Spencer,  Sociology,  I.  91),  I  do  not  see  how  it  can  be  denied 
that  he  is  ignorant  because  he  is  incapable  of  an  operation. 
And  if  that  operation  is  not  an  inference,  I  can  not  see  why 
anything  else  should  be  inference.  The  plain  and  palpable 
facts  of  the  case  will,  I  think,  be  too  hard  for  the  friends  of  the 
syllogism.  And  if  they  embrace  another  alternative,  and  find 
their  amusement  in  the  manufacture  of  majors,  which  would 
never  have  been  seen  if  the  arguments  had  not  come  first, 
then  I  think  once  more  that  the  end  must  be  near.  So  barren 
a  shift  will  be  the  dying  effort  of  a  hard- run  and  well-nigh 
spent  chimaera. 

But  there  is,  as  we  saw,  another  alternative ;  it  may 
perhaps  be  thought  possible  to  save  the  syllogism  by  first 
reforming  it.  Throw  the  major  premise  overboard,  and  call 
anything  a  syllogism  which  can  be  brought  into  the  form  of 
elements  related  within  one  whole.  But  if  the  friends  of  the 
syllogism  resolve  on  this  policy,  I  think  they  are  friends  it 
might  pray  to  be  saved  from.  It  is  better  to  bury  a  delusion 
and  forget  it  than  to  insult  its  memory  by  retaining  the  name 
when  the  thing  has  perished.  And  it  is  better  to  profess  that 
delusion  openly  than  ostensibly  to  abandon  all  but  the  name, 
and  then  covertly  to  re-instate  the  errors  it  once  stood  for. 
When  a  mistake  has  lasted  some  two  thousand  years  I  am 
ready  to  believe  that  it  must  contain  truth,  but  I  must  believe 
too  that  the  time  is  come  when  that  truth  should  be  able  to 
stand  by  itself  We  can  not  for  ever  with  eyes  fast  closed 
swallow  down  the  mass  of  orthodox  rubbish  in  which  that 
truth  has  wrapped  itself  up.  And  if  the  time  has  not  come  for 
extracting  the  kernel,  the  time  has  come  for  rejecting  the  shell. 

§  9.  But  if  the  principle  of  the  syllogism  is  not  the  axiom 
of  reasoning,  can  we  find  any  other  which  will  stand  the  test  ? 
We  shall  see  hereafter  that  the  logic  of '"  Induction "  is  no 
more  satisfactory.  We  shall  allude  to  the  doctrine  of  Mr. 
Spencer,  and  review  the  theory  of  Substitution  which  has 
found  an  advocate  in  Professor  Jevons.  For  the  present  it 
will  suffice  to  mention  a  principle  adduced  by  Mr.  Spencer, 
and  which  has  succeeded  in  gaining  the  authority  of  Wundt- 
"  Things  related  to  the  same  are  related  to  each  other  "  is 


CiiAr.  II.]  SOME   ERRONEOUS   VIEWS.  233 

the  axiom,  we  are  told,  of  all  valid  reasoning.  "  Where  judg- 
ments are  placed  in  relation  to  one  another  by  means  of  concep- 
tions they  possess  in  common,  the  other  conceptions,  which 
the  judgments  possess  but  do  not  possess  in  common,  must 
stand  themselves  too  in  relation  to  one  another,  and  that  relation 
is  expressed  in  a  new  judgment." — (Wundt,  Logik,  I.  282.) 

We  may  confine  ourselves  to  the  simpler  formula. 
"Related  to  the  same  are  related  to  each  other"  is  wide 
enough  to  cover  the  examples  we  have  given.  We  shall 
certainly  hereafter  have  occasion  to  question  if  it  is  wide 
enough  to  cover  all  possible  examples  (Book  III.  Part  I. 
Chap.  I.).  But  though  I  may  object  to  it  hereafter  as  being 
too  narrow,  I  must  object  to  it  here  because  it  is  too  wide. 
It  is  a  principle  of  falsehood  as  well  as  of  truth ;  "  A  runs 
faster  than  B  and  B  keeps  a  dog  (C),"  "A  is  heavier  than  B 
and  B  precedes  C,"  "A is  worth  more  than  B  and  B  is  on  the 
table  (C),"  or  "A  is  like  B  and  B  is  like  C."  You  may 
doubtless  extract  some  kind  of  inference  out  of  these  premises, 
but  you  can  hardly  go  from  them  to  any  definite  and  immediate 
relation  between  A  and  C. 

§  10.  It  is  true  no  doubt  that,  if  A  and  C  are  both  related 
to  a  common  term  B,  we  know  that  some  relation  must  exist 
between  them,  since  both  must  be  elements  in  one  world  of 
knowledge.  But  unfortunately  we  knew  thus  much  before, 
and  independent  of  the  relation  of  both  in  particular  to  B. 

And  again  in  defence  of  the  axiom  it  may  be  said.  In  "  A  is 
like  B  and  B  is  like  C  "  the  terms  are  ;/<?/ related  to  a  common 
third  term.  B  resembles  A  perhaps,  in  one  point  and  resembles 
C  in  another  different  one,  and  so  it  is  with  the  other  examples. 
It  is  not  in  so  far  as  B  keeps  a  dog  that  A  outstrips  him,  it  is 
not  the  B  which  has  a  place  in  time  which  is  heavier  than  A, 
B  is  on  the  table  in  one  capacity  and  is  worth  more  than  A  in 
an  other  and  different  one.  Thus  the  terms  related  are  not 
related  to  the  sa7ney  and,  if  they  were,  they  would  be  related 
to  each  other. 

The  defence  I  have  invented  points  towards  the  truth,  and 
yet  it  is  vitiated  by  a  fatal  mistake.  It  is  true  to  say  that  in 
every  relation  there  must  always  be  an  underlying  identity  ; 
that  relations,  such  as  those  of  space  and  time,  presuppose  a 


234  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  L 

common  character  in  the  things  they  conjoin.  And  it  is 
therefore  true  that,  if  a  third  term  B  stands  first  in  spatial 
relation  with  A  and  again  in  temporal  relation  with  B,  its 
character  in  those  two  relations  is  different.  Hence,  if  two 
relations  are  of  different  classes,  the  term  common  to  each  will 
so  far  not  be  the  same. 

But  this  line  of  argument,  if  we  follow  it  out,  will  make  an 
end  of  all  kinds  of  relation  {cf.  Chap.  VI.  §  6).  To  say  that 
when  A  is  related  to  B,  it  is  related  so  far  as  B  is  nought  else 
but  its  relation  to  A,  is  quite  suicidal.  And,  if  we  will  not  say 
that,  and  if  already  B  is  something  different  from  its  relation 
to  A,  on  what  ground  can  we  refuse  it  a  right  to  another 
relation  with  C,  when  at  all  events  it  has  one  point  in 
which  it  differs  from  A }  Let  us  try  to  see  clearly ;  the 
terms  of  a  relation  must  always  be  more  than  the  relation 
between  them,  and,  if  it  were  not  so,  the  relation  would  vanish. 
"A  is  equal  to  B,"  but  if  B  were  mere  quantitative  identity 
with  A,  we  should  have  no  equality ;  there  would  be  nothing 
but  A.  "A  is  the  same  as  B  or  different  in  quality,"  but  if  A 
and  B  were  not  both  different  and  the  same,  then  the  terms 
and  the  relation  would  all  disappear  together.  "  A  is  north 
of  B  or  prior  to  C  ; "  but  if  A,  B,  and  C  were  no  more  than 
mere  naked  positions  in  space  or  time,  they  would  not  be 
even  that,  and  their  relations  would  sink  to  utter  nothingness. 
There  always  must  enter  into  the  relation  something  more 
than  the  actual  relation  itself.  And  this  ■  being  admitted,  if 
you  deny  that  the  B,  which  for  instance  is  spatially  related  to 
C,  is  the  same  as  the  B  which  has  a  relation  in  time  with  A, 
you  must  be  taken  to  assert  that  in  the  relation  A-B  the 
character  of  B  is  perfectly  simple,  and  that  B  is  nothing  but 
that  which  constitutes  its  relation  in  time.  But,  if  so,  it  is 
nothing  which  can  be  related,  and  the  axiom  can  find  no 
possible  application. 

The  mistakes,  which  arise  from  a  too  wide  axiom,  may 
indicate  the  truth  that  related  to  the  same  are  not  related  to 
each  other  unless  they  are  related  under  certain  conditions. 
We  shall  return  to  this  point  in  Chapter  IV.,  and  the  following 
Chapter  will  endeavour  to  convey  some  general  idea  of  the 
nature  of  inference. 


(    235     ) 


CHAPTER  III. 

A   GENERAL  IDEA   OF  INFERENCE. 

§  I.  Every  inference  combines  two  elements  ;  it  is  in  the 
first  place  a  process,  and  in  the  second  place  a  result.  The 
process  is  an  operation  of^ynthesis  ;  it  takes  its  data  and  by 
ideal  construction  combines  them  into  a  whole.  *  The  result 
is  the  perception  of  a  new  relation  within  that  unity.  We  start 
with  certain  relations  of  elements  ;  by  virtue  of  the  sameness 
of  two  or  more  of  these  elements  we  unite  their  relations  in 
one  single  construction,  and  in  that  we  perceive  a  fresh  relation 
of  these  elements.  What  is  given  to  us  is  terms  conjoined; 
we  operate  on  these  conjunctions  and  put  them  together  into 
a  whole ;  and  the  conclusion  is  the  perception  of  two  terms  in 
relation,  which  were  not  related  before  the  operation.  Thus 
the  process  is  a  construction  and  the  result  an  intuition,  while 
the  union  of  both  is  logical  demonstration. 

§  2.  Demonstration  in  logic  is  not  totally  different  from 
demonstration  elsewhere ;  proof  is  only  one  kind  of  demon- 
stration. Logicians  however  seem  generally  not  to  be  aware 
of  this  fact.  When  the  mathematician  "  demonstrates "  a 
conclusion  the  logician  feels  uneasy,  though  he  can  not  deny 
that  the  conclusion  is  proved.  But  uneasiness  becomes 
protest  and  open  renunciation  when  he  attends  at  the  "  de- 
monstrations"  of  the  anatomist.  He  shudders  internally  at 
the  blasphemous  assertion  that  "  this  which  I  hold  in  my 
hand  "  is  "  demonstrated,"  But  his  trials  are  not  over ;  the 
illiterate  lecturer  on  cookery  overwhelms  him  by  publicly 
announcing  the  "  demonstration  "  of  an  omelette  to  the  eyes 
of  females. 

*  As  we  remarked  before,  the  statements  in  this  Book  are  subject  to 
correction  by  the  Book  that  follows. 


236  THE   PRINCIPLES  OF   LOGIC.  [Bk.  IL  Pt.  I. 

But  I  think  the  logician  has  no  real  cause  of  quarrel  even 
with  the  cook.  For  demonstration  is  merely  pointing  out 
or  showing  ;  and  if  the  conclusion  of  an  inference  is  seen 
and  thus  may  be  shown,  so  also  may  a  nerve  or  again  an 
omelette.  It  is  useless  to  deny  this,  and  the  task  of  the 
logician  is  to  distinguish  inference  from  other  kinds  of  demon- 
stration. 

§  3.  When  in  ordinary  fact  some  result  can  be  seen  and  is 
pointed  out,  perhaps  no  one  would  wish  to  call  this  "  demon- 
stration." It  is  mere  perceiving  or  observation.  It  is  called 
demonstration  when,  to  see  the  result,  it  is  necessary  for  us 
first  to  manipulate  the  facts ;  when  you  show  within  and  by 
virtue  of  a  preparation  you  are  said  to  demonstrate.  But  if 
the  preparation  experiments  outwardly,  if  it  alters  and  ar- 
ranges the  external  facts,  then  the  demonstration  is  not  an 
inference.  It  is  inference  where  the  preparation  is  ideal^  where 
the  rearrangement  which  displays  the  unknown  fact  is  an 
operation  in  our  heads.  To  see  and,  if  it  pleases  us,  also  to 
show  a  new  relation  of  elements  in  a  logical  construction  is 
demonstration  in  the  sense  of  reasoning. 

§  4.  In  what  does  this  mental  preparation  consist }  We 
have  seen  in  our  account  of  the  synthetic  judgment  its  general 
character.  It  demands  in  the  first  place  certain  data;  it 
must  have  two  or  more  connections  of  elements,  as  A  — B 
B  —  C  C  —  D  ;  and  these  are  the  premises.  It  is  necessary  again 
that  these  premises  should  be  judgments  actual  or  suggested, 
and  what  they  assert  or  suppose  must  consist  in  logical 
connections  of  content.  For  if  the  data  consisted  of  unrefined 
sensuous  material,  or  were  mere  imaginations,  the  result  would 
be  sensuous  or  merely  imaginary ;  it  would  be  a  psycholo- 
gical effect  and  not  a  logical  consequence.  The  premises  are 
thus  so  far  two  or  more  judgments,  and  the  operation  on 
these  data  will  consist  in  joining  them  into  a  whole.  We 
must  fasten  them  together,  so  that  they  cease  to  be  several 
and  are  one  construction,  one  individual  whole.  Thus  instead 
of  A-B  B-C  we  must  have  A~B-C. 

Now  if  this  were  done  arbitrarily  it  would  not  be  done 
logically,  and  we  should  have  no  reason  to  think  the  result 
true.     If  wc  took  A-B  and  C-D  and  joined  them  together 


Chap.  III.]  A   GENERAL   IDEA   OF   INFERENCE.  237 

as  A  -  B  -  C  -  D,  our  procedure  would  be  as  futile  as  if  in 
anatomy  we  showed  connections  by  manufacturing  them,  or 
as  if  in  order  to  clear  a  preparation,  we  employed  some  agent 
which  radically  changed  it.  In  relation  to  fact  our  results 
in  this  case  would  be  invalid.* 

We  can  not  logically  join  our  premises  into  a  whole  unless 
they  offer  us  points  of  connection.  But  if  the  terms  between 
which  the  relations  subsist  are  all  of  them  different  we  are 
perfectly  helpless,  for  we  can  not  make  an  arch  without  a 
key-stone.  Hence,  if  we  are  to  construct,  we  must  have  an 
identity  of  the  terminal  points.  Thus,  in  A  —  B  B  —  C,  B 
is  the  same  and  we  connect  A  —  B  —  C;  in  A  —  B  —  C  and 
C  — D,  C  is  the  same  and  we  connect  A  — B  — C  — D.  The 
operation  consists  in  the  extension  and  enlargement  of  one 
datum  by  others,  by  means  of  the  identity  of  common  links. 
And  because  these  links  of  union  were  given  us,  therefore  we 
assume  that  our  construction  is  true  ;  although  we  have  made 
it  yet  it  answers  to  facts. 

Having  thus  turned  our  premises  into  one  whole,  we 
proceed,  to  our  conclusion  by  mere  inspection.!  If  A  — B  — 
C  — D  is  true  of  reality,  then  in  that  we  can  see  A— C  or 
A  — D,  or  again  B  — D,  relations  which  previously  we  did 
not  know.  Then,  leaving  out  of  view  those  parts  of  our 
construction  in  which  we  are  not  interested,  we  extract  the 
conclusion  we  desire  to  assert.  We  first  do  a  certain  work 
on  our  data;  and  this  work  is  the  construction.  We  then 
by  inspection  discover  and  select  a  new  relation,  and  this 
intuition  is  the  conclusion. 

§  5.  I  will  illustrate  the  above  by  several  examples.  Take 
three  pictures  on  a  wall  A,  B,  and  C  ;  if  I  see  them  all  at 
once  as  A  —  B  —  C  there  seems  so  far  no  inference,  for  my 
mere  analytic  judgment  will  give  me  A  — C  (Book  I.  Chap. 
II.).  But  suppose  I  see  first  A  -  B,  and  then  afterwards  B  —  C, 
no  mere  analysis  will  give  me  A-C.  I  must  first  put  them 
together  as  A  —  B  —  C,  and  this  is  the  construction  of  a  syn- 
thetic judgment.     I    then   perceive   A  — C,   and   this   is   the 

*  All  this  is  subject  to  correction  by  Book  III. 

t  I  omit  to  consider  here  the  selective  action.  That  is  not  of  the 
essence  of  all  inference.     Vid.  Book  III.  Part  I.  Chap.  I. 


238  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  L 

conclusion,  which  is  inferred  not  because  it  is  seen  in  fact, 
but  seen  in  my  head. 

Let  us  take  an  instance  from  geographical  position.  A  is 
ten  miles  north  of  B,  B  is  ten  miles  east  of  C,  D  is  ten  miles 
north  of  C ;  what  is  the  relation  of  A  to  D  .?  If  I  draw 
the  figure  on  a  piece  of  paper  that  relation  is  not  inferred  ; 
but  if  I  draw  the  lines  in  my  head,  in  that  case  I  reason. 
In  either  case  we  employ  "  demonstration,"  but  only  in  the 
latter  do  we  demonstrate  logically. 

"A  =  B  and  B  =  C  therefore  A  =  C."  In  this  argument 
there  is  no  demonstration  to  sense,  for  the  showing  is  ideal. 
The  terms  are  put  together  through  the  sameness  of  B,  and 
are  combined  into  a  whole  united  by  the  relation  of  quan- 
titative identity.  The  whole  is  a  series  united  by  that 
character,  and  here  is  the  construction.  We  then  inspecting 
the  series  find  a  new  relation  A  —  C,  and  here  is  the  conclusion. 

Take  an  example  we  have  given  in  Chapter  I.  ;  if  three 
strings  A,  B,  and  C  are  struck  together  and  we  hear  that  they 
all  produce  the  same  note,  we  hardly  infer  that  they  are  in 
tune  with  one  another.  But  first  strike  A  and  B,  and  then 
strike  B  and  C  ;  on  this,  if  A  and  B  have  no  difference  in 
note,  and  B  and  C  have  no  difference  in  note,  I  proceed  to 
construct  the  ideal  group  of  ABC  united  throughout  by 
sameness  of  note.  This  is  a  mental  synthesis,  and  a  mere 
analytical  perception  then  adds  that  A  and  C  are  in  tune 
with  one  another. 

We  may  see  this  again  in  an  ordinary  syllogism.  We 
must  not  state  it  so  as  to  beg  the  question,  or  to  have  no 
common  term,  but  may  state  it  thus,  "  Man  is  mortal  and 
Caesar  is  man  and  therefore  Caesar  is  mortal."  There  is  first 
a  construction  as  Caesar-man-mortal,  and  then  by  inspection 
we  get  Caesar-mortal. 

§  6.  It  is  useless  to  attempt  to  lay  down  rules  for  either 
part  of  this  process.  It  is  the  man  who  perceives  the  points 
of  union  within  his  premises — who  can  put  (as  the  saying  is) 
two  and  two  together — who  is  able  to  reason.  And  so  long 
as  he  secures  the  unity  of  his  ^  construction  he  has  reasoned 
rightly.  In  the  next  Chapter  we  shall  see  that  no  models 
for   construction   can    possibly   be   invented.      And    for    the 


Chap.  III.]  A   GENERAL   IDEA   OF   INFERENCE.  239 

process  of  inspection  one  wants  a  good  eye  ;  for  there  are  no 
rules  which  can  tell  you  what  to  perceive. 

We  must  free  ourselves  from  these  superstitions,  if  we  can, 
and  there  are  others  beside  which  have  oppressed  us  too  long. 
It  is  ridiculous  for  instance  to  think  about  the  order  of  our 
premises.  The  construction  when  made  need  have  no  order 
in  time,  and  the  order  of  its  making  may  be  left  entirely  to 
private  convenience  or  else  to  chance. 

And  there  is  another  superstition  we  may  here  dispose 
of.  The  number  of  terms  is  not  limited  to  three.  In  the 
geographical  example   of  the   previous  section  we  certainly 

jA  AD     /A     D A 

do  not  argue  thus  p !-„  . ' .  Q^^^^   ,  and      /        .  * .  , 

D|        |A 

but  we   first  complete   our   construction    | I     ,    and  then 

C  B 
go  to  D A.  It  is  true  no  doubt  that  in  making  a  con- 
struction we  are  forced  to  establish  one  link  at  a  time  ; 
but  it  is  wholly  false  that  we  are  compelled  to  conclude 
before  we  take  in  another  premise.  Logic  sets  no  limit  to 
the  number  of  premises  which  may  precede  the  conclusion, 
and  it  is  the  weakness  of  our  heads  which  narrows  our  con- 
structions and  narrows  them  sometimes  to  the  prejudice 
of  our  inference.  There  is  no  branch  of  science  where  con- 
structive power  is  wholly  uncalled  for,  and  certainly  some 
where  it  is  of  the  first  importance.  And  perhaps  we  may 
say  without  exaggeration  that  a  man,  who  can  not  use  more 
than  three  terms  in  reasoning,  is  unlikely  to  do  much  in  any 
subject.  But,  however  that  may  be,  the  limit  is  psychological 
and  is  not  logical. 


240  THE    PRINCIPLES   OF   LOGIC.  .  [Bk.  IT.  Pr.  J. 


CHAPTER  IV. 

PRINCIPLES  OF  REASONING. 

§  I.  We  have  seen  in  outline  the  main  character  of  in- 
ference and  we  naturally  recur  to  a  former  question,  Is 
there  any  axiom  or  principle  of  reasoning  ?  The  result  of 
our  enquiry  in  the  Second  Chapter  was  that  we  could  find 
nothing  quite  satisfactory.  The  syllogistic  rnaxims  ^were  all 
too  narrow,  and  the  axiom  that  "  Things  whi5j^^|' related  to 
the  same  are  related  to  each  other,"  we  fo^^f^  the  other 
hand  was  much  too  wide.  It  may  serve  us/nowever  as  a 
point  of  departure.  When  properly  restricted  it  will  express 
the  truth,  so  far  as  is  required  by  the  present  Book. 

I  will  repeat  the  result  we  arrived  at  before.  The  principle 
that  elements  which  stand  in  relation  to  a  common  point  are 
themselves  related,  is  not  the  actual  principle  that  operates  in 
any  given  special  inference.  In  its  abstract  form  it  is  useless 
for  the  purp'ose  of  getting  a  conclusion.  It  assures  us,  before 
any  construction  is  made,  that  anything  which  we  have  as  an 
element  of  knowledge  stands  in  some  relation  with  every 
other  element.  But  it  will  not  enable  us  to  go  beyond  this, 
and  by  combining  our  premises  to  get  a  definite  relation.  If 
A  is  prior  to  B  in  time,  and  B  is  west  of  C  in  space,  then  on 
the  strength  of  B  we  can  put  these  together,  but  we  can  not 
by  means  of  our  combination  get  a  definite  relation  of  A  to 
C.  We  knew  long  ago  that  A  and  C  co-existed  as  members 
within  the  universe  of  knowledge,  and  we  desire  to  learn  now 
not  that  general  connection,  but  some  special  attitude  of  A  to 
C.  But  in  order  to  get  this,  and  to  be  able  so  to  speak  to 
draw  a  new  line  from  A  to  C,  it  is  necessary  first  to  connect 
A  and  C  in  a  special  manner.  They  must  be  interrelated  not 
generally  and  in  the  universe  at  large,  but  in  some  special 


Chap.  IV.]  THE   PRINCIPLES   OF   REASONING.  24I 

world.  If  one  is  merely  in  time  and  the  other  merely  in  space, 
they  have  so  far  not  ^ot  an^  binding  centre.  To  be  specially 
related  they  must  be'r$lat^d  to  the  same,  and  under  conditions 
which  secure  an  unit j^f Construction. 

If  what  operat^yjBterence  is  the  principle  of  the  indi- 
viduality of  synthel^^^Baxiom  of  that  operation  must  not 
be  taken  too  widel^BPPat  the  cost  of  clumsiness  we  must 
state  it  in  two  faeces.  "  Where  elements  A  and  C  are  related 
homogeneously  to  a  common  B,  A  and  C  are  related  within 
the  same  genus.  Or  where  one  relation  only  (either  A  — B 
or  B  — C)  is  within  the  category  of  subject  and  attribute, 
there  is  a  valid  conclusion  within  the  category  of  either 
A  —  B  or  B  —  C."  To  express  the  same  otherwise,  "  There  is 
no  conclusion  where  the  relations  are  heterogeneous  unless 
one  of  the  two  joins  an  attribute  to  a  subject.  In  the  latter 
case  an  inference  is  possible  even  outside  the  category  of 
subject  and  attnibjite." 

§  2.  We^fpiijn^  fi^t  in  our  examination  of  the  syllogism 
that  there  wj|||^B^-ences  which  fell  outside  its  single  cate- 
gory of  subj^^^^B  attribute.  We  found  again  that  if  we 
kept  outside  T^PIpecial  categories,  mere  interrelation  was 
much  too  vague  to  form  a  bond.  The  conclusion,  which  in 
the  next  place  naturally  offers  itself,  is  that  inference  must 
take  place  within  several  special  categories  (such  as  time, 
space,  subject  and  attribute,  &c.)  but  must  always  be  confined 
in  each  case  to  one  category.  To  get  a  relation  of  time  in 
the  conclusion  you  would  have  to  keep  in  your  premises  to 
time-relations,  and  the  same  thing  again  with  other  kinds  of 
relation.  And,  if  this  were  true,  the  axiom  would  run, 
"  Things  related  to  the  same  within  one  kind  will  be 
interrelated  within  that  kind." 

But  there  are  inferences  which  will  not  submit  to  this 
principle.  "  Gold  is  heavier  than  lead  and  lead  is  a  metal," 
"  A  runs  faster  than  B  and  B  is  twice  as  tall,"  "  A  is  stronger 
than  B  and  B  is  full  grown,"  "  A  is  equal  to  B  in  weight  and 
B  is  moved  with  such  or  such  velocity  "  are  premises  which 
certainly  will  yield  conclusions,  and  yet  their  relations  are 
heterogeneous.  And  this  shows  that  we  may  cross  from 
category  to  category.     On  the  other  hand  we  are  unable  to 

R 


242  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  L 

do  this  unless  there  exists  a  special  condition  ;  one  relation 
must  be  that  of  attribute  to  subject.  From  "  A  is  equal  to 
B  and  B  has  such  velocity  "  we  have  seen  you  can  not  get  to 
the  conclusion  "  A  has  such  velocity."  You  can  not  do  so  till 
you  predicate  of  A  that  point  in  B  which  brought  it  into 
relation  with  the  other  element  (C).  And  from  "  A  is 
equal  to  B  and  B  is  in  my  pocket "  you  can  not  infer  that  A 
is  in  my  pocket,  since  the  spatial  relation  which  is  affirmed 
of  B  is  not  true  of  B  as  equal  to  A.  You  can  not  argue  t*o  a 
relation  of  A  to  my  pocket,  but  your  conclusion  must  be 
"  A  is  equal  to  something  which  is  in  my  pocket."  We  have 
still  the  old  relation  of  A  to  B,  but  qualified  by  the  addition 
of  an  adjective  of  B.  And  it  is  true,  I  think,  in  all  possible 
cases  that  the  relation  between  a  subject  and  attribute  is  the 
only  one  which,  if  used  with  another  category,  is  able  to  give 
us  a  new  relation.* 

The  remarks  we  let  fall  in  a  previous  chapter  (II.  §  7) 
may  have  prepared  the  reader  for  our  result.  The  categories 
do  not  stand  on  one  and  the  same  footing.  It  is  possible 
after  all  to  express  unconditionally  the  principle  of  inference, 
and  it  is  possible  to  do  this  within  the  one  category  of  subject 
and  attribute  (p.  271).  But  we  are  not  yet  arrived  at  the  stage 
where  this  is  possible,  and  must  content  ourselves  here  with 
the  formula  that  ended  the  foregoing  section,  "  Related  to  the 
same  within  the  same  kind  are'  interrelated  within  that  kind," 
with  a  further  axiom  of  possible  inference  where  one  relation 
is  that  of  subject  to  attribute. 

§  3.  Our  main  principle,  it  is  obvious,  will  have  as  many 
forms  as  there  happen  to  be  categories  or  kinds  of  relation. 
It  is  not  the  business  of  this  work  to  elaborate  any  theory  as 
to  how  these  kinds  are  connected  or  are  subordinated.  It  is 
again  not  our  purpose  to  draw  out  and  defend  a  complete 
enumeration   or   scheme   of  such   classes.     But   in   order  to 

*  Other  examples  are  "  A  has  a  voice  (B),  that  voice  overpowers  Z's 
voice  (C),  therefore  A  overpowers  C."  "  A  has  a  voice  (B)  which  is  in  tune 
with  C,  therefore  A  has  something  in  tune  with  C."  In  the  first  of  these 
the  relation  of  the  conclusion  is  hardly  between  a  subject  and  attribute. 
A  by  virtue  of  its  attribute,  which  attribute  acquired  a  momentary  indepen- 
dence, has  got  a  new  relation  to  another  subject. 


Chap.  IV.]  THE   PRINCIPLES   OF   REASONING.  243 

make  clear  the  general  result,  I  will  state  and  illustrate  four 
or  five  main  principles  which  operate  in  inference.  We  may 
call  them  the  principles  (i)  of  the  synthesis  of  subject  and 
attribute,  (ii)  of  identity,  (iii)  of  degree,  (iv)  of  space,  and  (v) 
of  time. 

I.  Prmciple  of  synthesis  of  subject  and  attribute. 
(a)  The  attributes  of  one  subject  are  interrelated. 

(y8)  Where  two  subjects  have  the  same  or  a  different 
attribute  they  are  alike  or  different. 

(7)  (i)  Where  the  attribute  is  not  taken  as  distinct  from 
every  subject,  what  is  asserted  of  the  attribute  is  asserted  of 
its  subject,  (ii)  Where  the  subject  is  not  taken  as  distinct 
from  every  attribute,  what  is  affirmed  of  the  subject  is  affirmed 
of  any  attribute  considered  as  its  attribute. 

Examples,  (a)  This  man  is  a  logician,  this  man  is  a  fool, 
therefore  a  logician  may  be  *  (under  some  conditions  is)  a  fool. 

(/3)  This  dog  is  white,  this  horse  is  white  (or  brown),  this 
dog  and  this  horse  are  alike  (or  different). 

(7)  (i)  This  figure  is  a  triangle,  a  triangle  has  the  angles 
equal  to  two  right  angles,  this  figure  has  the  angles  equal  to 
two  right  angles.  (ii)  Gold  is  heavier  than  lead  ;  lead  is  a 
metal.  Therefore  lead-metal  (or  some  metal)  is  lighter  than 
gold,  or  metal  may  be  lighter  than  gold. 

I  may  remark  on  (7)  that,  if  we  were  to  say  "  What  is  true 
of  the  attribute  is  true  of  the  subject,  and  what  is  true  of  the 
subject  is  true  of  the  attribute,"  we  should  fall  into  an  error. 
The  subject  qua  subject  and  the  attribute  qua  attribute  have 
each  predicates  which  can  not  be  applied  to  the  other.  Thus 
"  Iron  is  heavy,  heavy  is  a  quality  "  is  no  ground  for  the  asser- 
tion "  Iron  is  a  quality,"  nor  from  "  Iron  is  heavy,  iron  is  a 
substance,"  can  you  go  to  the  conclusion  "  Heavy  may  be  a 
substance"  (cf  Book  I.  Chap.  III.  §  10).  If  on  the  other 
hand  we  laid  down  as  a  condition  of  the  inference  that  this 
attribute  and  this  subject  must  be  taken  together,  we  should 
then  have  become  circular. 

II.  Synthesis  of  Identity. 

Where  one  term  has  one  and  the  same  point  in  common 

*  May  be  because,  the  subject  being  undefined,  the  conditions  are 
partly  unknown.     Vid.  Book  I.  Chap.  VII.  §  26. 

R    2 


244  THE   PRINCIPLES   OF   LOGIC.  [Bi.  II.  Pt.  L 

with  two  or  more  terms,  there  these  others  have  the  same 
point  in  common. 

Examples.  "Coin  A  has  the  same  inscription  as  coin  B, 
and  coin  B  as  coin  C,  therefore  A  as  C  ; "  "  Instrument  A  is 
in  tune  with  my  tuning-fork  (B),  and  so  too  are  instruments 
C  and  D,  therefore  they  are  all  in  tune  with  one  another  ;  " 
"  If  A  is  the  brother  of  B,  and  B  of  C,  and  C  is  the  sister  of 
D,  then  A  is  the  brother  of  D." 

III.  Synthesis  of  Degree. 

When  one  term  does,  by  virtue  of  one  and  the  same  point 
in  it,  stand  in  a  relation  of  degree  with  two  or  more  other 
terms,  then  these  others  also  are  related  in  degree. 

Examples.  "  A  is  hotter  than  B  and  B  than  C,  therefore  A 
than  C  ; "  "  Colour  A  is  brighter  than  B  and  B  than  C, 
therefore  A  than  C  ; "  "  Sound  A  is  lower  in  tone  than  B  and 
B  than  C,  therefore  A  than  C."  I  will  not  enquire  here 
whether  "  A  =  B  and  B  =  C,  therefore  A  =  C,"  falls  under  this 
head  or  under  the  previous  head  of  the  synthesis  of  identity. 

IV.  and  V.  Syntheses  of  Time  and  Space. 

Where  one  and  the  same  term  stands  to  two  or  more 
other  terms  in  any  relation  of  time  or  space,  there  we  must 
have  a  relation  of  time  or  space  between  these  others. 

Examples.  "  A  is  north  of  B  and  B  west  of  C,  therefore  C 
south-east  of  A  ; "  "  A  is  a  day  before  B,  B  contemporary  with 
C,  therefore  C  a  day  after  A." 

This  list,  as  we  have  said,  does  not  pretend  to  be 
complete,  and  it  would  not  be  possible  for  us  here  to  discuss 
the  questions  which  any  such  pretence  would  at  once  give 
rise  to.  Take  for  instance  the  synthesis  of  cause  and  effect. 
Does  this  fall  entirely  under  the  head  of  time  ?  Does  it  fall 
under  the  head  of  subject  and  attribute  }  Does  it  fall  under 
both  or  again  under  neither  ?  The  answers  to  these  questions 
would  be  hard  to  get,  and,  if  we  got  them,  they  would  be  of 
no  use  to  us  here.  They  would  not  much  serve  to  confirm 
the  result  we  already  have  reached  ;  they  would  possibly 
supply  one  more  illustration,  where  I  hope  enough  have 
already  been  given. 

§  4.  But  there  is  another  question  which  can  not  be 
passed  by.     We  have   called   these   syntheses  Principles  of 


Chap.  IV.]  THE   PRINCIPLES   OF   REASONING.  245 

inference,  and  have  ejected  the  syllogism  to  enthrone  them  in 
its  stead.  But  how  are  we  to  understand  the  title  they  lay  claim 
to  ?  We  know  what  the  syllogism  tried  to  accomplish,  for  it 
professed  to  control  from  a  central  office  every  possible  event 
in  all  parts  of  its  kingdom.  It  issued  some  two  dozen  forms 
of  reasoning,  to  which  all  inference  was  expected  to  con- 
form. Thus  you  had  always  some  model  with  relations  ready 
drawn  between  all  the  terms  both  in  premises  and  conclusion, 
and  no  liberty  was  left  you  save  to  fill  up  the  blanks  with 
terms  of  your  own.  The  moods  and  figures  were  a  bed  of 
Procrustes  into  which  all  arguments  had  somehow  to  be 
forced,  and  they  were  therefore  not  merely  principles  of 
reasoning,  but  actual  canons  and  tests  of  inference.  Within 
this  pale  you  were  secure  of  salvation,  and  on  the  outside  it 
was  heresy  to  doubt  you  were  lost.  Such  was  the  claim 
which  the  syllogism  put  forth,  and  enforced  as  long  as  it  had 
any  strength. 

Like  some  other  chim?eras  that  have  had  their  day,  the 
syllogism  is  effete  and  its  realm  is  masterless ;  and  the 
question  for  us  who  aspire  to  the  inheritance  is  to  know  in 
what  character  we  mean  to  succeed.  Do  we  wish  to  sub- 
stitute one  despotism  for  another }  Are  our  principles  of 
inference  to  be  tests  and  canons  ?  Most  assuredly  not ;  for 
if  the  thing  were  desirable,  and  I  am  much  too  staunch  a 
Protestant  to  desire  it,  it  is  at  all  events  thoroughly  impossible. 

§  5.  Our  principles  give  us  under  each  head  of  inference 
the  general  and  abstract  form  of  the  operation.  They  do  not 
profess  in  all  cases  to  give  us  the  individual  operation  itself 
which  is  necessary.  It  is  not  merely  that  the  terms  are  left 
blank,  for  the  special  relations  of  the  premises  and  conclusion 
are  also  left  blank.  The  kind  of  construction  is  indicated 
generally,  and  the  kind  of  conclusion  you  will  find  within  it ; 
but  the  actual  construction,  and  the  actual  new  relation  to 
which  that  will  give  rise,  are  left  entirely  to  private  judgment. 

From  such  premises  as  "  A  to  the  right  of  B  and  B  to  the 
right  of  C,"  there  is  and  there  can  be  no  form  of  reasoning 
which  will  give  you  the  conclusion.  It  is  true  that  the  axiom 
goes  so  far  as  to  assure  you  that  A  and  C  must  be  related  in 
space,  for  you  do  not  know  that  unless  you  know  that  the 


246  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  L 

two  Space-relations  belong  to  one  world.  And  you  do  not 
know  this  unless  you  are  sure  that  they  have  a  common 
meeting-point  in  space  (Book  I.  Chap.  II.  §  21).  But  the 
axiom  will  not  tell  you  anything  beyond.  It  will  neither  give 
you  the  definite  relation,  nor  even  assure  you  that  you  will  be 
able  to  attain  to  any  such  relation.  A  is  greater  than  B,  and 
C  is  greater  than  B,  therefore  (if  the  point  in  B  is  the  same) 
A  and  C  must  certainly  be  related  in  degree ;  but  you  do  not 
know  how.  B  is  south  of  both  A  and  C,  therefore  A  and  C  are 
related  in  space ;  but  you  have  no  means  of  getting  to  know 
their  particular  relation.  For  the  individual  construction  can 
not  here  be  drawn,  and  it  is  that  alone  which  can  supply  the 
conclusion. 

Where  the  inference  is  valid,  the  special  operation  by 
which  it  is  performed  falls  outside  the  axiom,  and  it  is 
impossible  therefore  that  the  axiom  can  supply  any  test  of 
validity.  Where  the  inference  is  invalid,  what  makes  it 
invalid  may  fall  without  the  axiom,  and  the  axiom  is  there- 
fore no  test  of  invalidity.  If  I  like  to  argue  that,  because  A 
and  C  are  both  greater  than  B,  they  are  equal  to  one  another, 
the  principle  has  nothing  to  say  against  it.  If  I  choose  to  go 
from  "  B  is  south  of  both  A  and  C  "  to,  "  therefore  A  and  C 
lie  east  and  west,"  again  the  principle  is  perfectly  satisfied. 
It  can  no  more  tell  me  that  here  I  am  wrong  than  that  I  am 
right  if  I  say,  "  A  is  due  north-west  of  C,  because  B  is  five 
miles  south  of  A  and  again  the  same  distance  west  of  C." 
The  general  form  is  valid  in  either  case,  but  the  actual 
operation,  whether  erroneous  or  correct,  is  in  either  case 
beyond  the  scope  of  the  principle.  It  is  not  a  matter  for 
superior  direction  ;  it  is  a  matter  for  private  inspiration  and 
insight. 

§  6.  It  is  impossible  that  there  should  be  fixed  models  for 
reasoning  ;  you  can  not  draw  out  exhaustive  schemata  of  valid 
inference.  There  are  principles  which  are  tests  of  the  general 
possibility  of  making  a  construction :  but  of  the  actual 
construction  there  can  be  no  canons.  The  attempt  to 
manufacture  them  would  lead  to  the  search  for  a  completed 
infinity  ;  for  the  number  of  special  relations  has  no  end,  and 
the  possible  connections  in  time  space  and  degree  are  indefinite 


CiiAP.  IV.]  THE   PRINCIPLES   OF   REASONING.  247 

and  inexhaustible.  To  find  the  canons  of  valid  inference  you 
must  first  make  a  list  of  valid  inferences.  You  will  manufacture 
a  major  premise  for  each,  and  that  major  premise  derived  from 
each  operation  will  appear  as  its  canon.  Your  success,  if  you 
succeeded,  would  be  the  capture  of  a  phantasm,  but  in  the 
endlessness  of  the  field  you  would  be  for  ever  eluded.  No 
canon  will  fix  for  us  the  pale  of  orthodoxy,  until  that  day 
comes  when  the  nature  of  things  will  change  itself  to  gratify 
our  stubborn  illusions. 

§  7.  The  popular  belief  in  logic  endows  it  with  ability  to 
test  all  reasonings  offered  it.  In  a  given  case  '  of  given 
premises  the  logician  is  thought  to  be  a  spiritual  Director  who, 
if  he  can  not  supply,  at  least  tests  right  and  wrong.  Thus,  if 
logic  is  no  art  which  provides  us  with  arguments,  yet,  once 
give  it  the  premises,  and  it  is  both  the  art  of  extracting 
conclusions  and  of  assaying  all  those  which  amateurs  have 
extracted  without  its  authority.  But,  understood  in  this  sense, 
logic  has  no  existence,  for  there  is  and  there  can  be  no  art 
of  reasoning.  Logic  has  to  lay  down  a  general  theory  of 
reasoning,  which  is  true  in  general  and  in  the  abstract.  But 
when  it  goes  beyond  that,  it  ceases  to  be  a  science,  it  ceases 
to  be  logic,  and  it  becomes,  what  too  much  of  it  has  already 
become,  an  effete  chimaera  which  cries  out  for  burial. 

§  8.  It  should  not  lie  alone.  There  is  another  false  science 
more  unlovely  in  life  and  more  unpleasant  in  decay,  from 
which  I  myself  should  be  loath  to  divide  it.  Just  as  Logic  has 
been  perverted  into  the  art  of  reasoning,  so  Ethics  has  been 
perverted  into  the  art  of  morality.  They  are  twin  delusions 
we  shall  consign,  if  we  are  wise,  to  a  common  grave. 

But  I  would  not  grudge  Casuistry  a  Christian  burial.  I 
should  be  glad  to  see  it  dead  and  done  with  on  any  terms  ;  and 
then,  if  all  the  truth  must  be  spoken,  in  its  later  years  it  has 
suffered  much  wrong.  That  it  became  odious  beyond  parallel 
and  in  parts  most  filthy,  is  not  to  be  denied  ;  but  it  ill  becomes 
the  parents  of  a  monster,  who  have  begotten  it  and  nourished 
it,  to  cry  out  when  it  follows  the  laws  of  its  nature.  And,  if  I 
am  to  say  what  I  think,  I  must  express  my  conviction  that  it 
is  not  only  the  Catholic  priest,  but  it  also  is  our  Utilitarian 
moralist,  who  embraces  the  delusion  which  has  borne  such  a 


248  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  L 

progeny.  If  you  believe,  as  our  Utilitarian  believes,  that  the 
philosopher  should  know  the  reason  why  each  action  is  to  be 
judged  moral  or  immoral ;  if  you  believe  that  he  at  least 
should  guide  his  action  reflectively  by  an  ethical  code,  which 
provides  an  universal  rule  and  canon  for  every  possible  case, 
and  should  enlighten  his  more  uninitiated  fellows,  then  it 
seems  to  me  you  have  wedded  the  mistake  from  which  this 
offensive  offspring  has  issued.  It  may  be  true  that  the  office 
of  professional  confessor  has  made  necessary  a  completer 
codification  of  offences,  and  has  joined  doctrinal  vagaries  to 
ethical  blunders.  We  may  allow  that  it  was  the  lust  for 
spiritual  tyranny  which  choked  the  last  whisper  of  the 
unsanctified  conscience.  It  may  be  true  that,  in  his  effort 
theoretically  to  exhaust  the  possibilities  of  human  depravity, 
the  celibate  priest  dwelt  with  curious  refinement  on  the  morbid 
subject  of  sexual  transgression.  But  unless  his  principle  is 
wholly  unsound  I  confess  that  I  can  hardly  find  fault  with  his 
practice  ;  for  if  there  is  to  be  an  art  and  a  code  of  morality, 
I  do  not  see  how  we  can  narrow  its  scope  beforehand.  The 
field  is  not  limited  by  our  dislikes,  and  whoever  works  at 
the  disgusting  parts,  is  surely  deserving  not  of  blame  but  of 
gratitude.  Hence  if  the  Utilitarian  has  declined  to  follow 
the  priest,  he  has  also  declined  to  follow  his  own  principles  ; 
he  has  stopped  short  not  from  logical  reasons  but  from 
psychological  causes. 

§  9.  It  is  natural  to  think  that  logic  has  to  tell  us  how  we 
are  to  reason  from  special  premises ;  and  it  is  natural  to  think 
that  ethics  must  inform  us  how  we  are  to  act  in  particular 
cases.  Our  uncritical  logic  and  our  uncritical  ethics  naturally 
assume  these  doctrines  as  self-evident.  But  the  mistake,  if 
natural,  is  in  both  cases  palpable.  Unless  you  artificially 
limit  the  facts,  then  models  of  reasoning  can  not  be  procured, 
since  you  would  need  in  the  end  an  infinitude  of  schemes  to 
parallel  the  infinitude  of  possible  relations.  And  a  code  of 
morality  is  no  less  impossible.  To  anticipate  the  conclusion 
in  each  special  case  you  would  have  to  anticipate  all  possible 
cases  ;  for  the  particular  condition  which  makes  this  conduct 
right  here  and  wrong  elsewhere,  will  fall  outside  the  abstrac- 
tions of  the  code.     You  are  thus  committed  to  a  dilemma :  at 


Chap.  IV.]  THE   PRINCIPLES   OF   REASONING.  249 

a  certain  point  you  must  cease  to  profess  to  go  right  by  rule, 
or  else,  anticipating  all  possible  combinations  of  circumstances, 
you  must  succeed  in  manufacturing  countless  major  premises. 
The  second  alternative  is  in  the  first  place  illusory,  since  the 
principle  is  really  got /r^w  the  intuition,  and  in  the  next  place 
it  is  impossible,  since  the  number  of  principles  will  be  limit- 
less and  endless.  But  if  you  accept  the  first  alternative,  and 
admit  that  only  in  certain  cases  it  is  possible  to  deduce  the 
conclusion  from  a  principle,  you  have  given  up  the  hope  of  your 
"practical  reason,"  and  denied  the  axiom  from  which  you  set  out. 

The  syllogistic  logic  possesses  one  merit.  If  its  basis  is 
mistaken  and  its  conclusion  false,  at  least  it  has  not  stopped 
short  of  its  goal.  In  Barbara  Celarent  its  code  is  perfected, 
and  it  has  carried  out  the  purpose  with  which  it  began.  We 
can  not  say  so  much  of  the  Casuistry  of  Hedonism.  The 
confident  dogmatism  of  its  setting-out  has  been  lost  in 
vagueness  and  in  hesitation.  It  flies  to  ambiguities  it  does 
not  venture  to  analyze,  and  sighs  faintly  to  a  Deity  which  it 
dares  not  invoke.  But  if  the  principle  of  our  most  fashionable 
Ethics  is  true,  then  an  art  of  Casuistry  and  a  Science  of  Sin  are 
the  goal  of  that  Ethics,  and  the  non-recognition  of  this  evident 
result,  if  creditable  to  the  heart,  does  no  honour  to  the  head. 
If  the  popular  moralist  will  not  declare  for  a  thorough-going 
Casuistry,  if  he  retires  in  confusion  from  the  breath  of  its 
impurity,  he  should  at  least  take  courage  to  put  away  the 
principles  which  have  given  it  life.  We  may  apply  to  him  as 
he  stands  a  saying  of  Strauss,  "  He  partly  does  not  know 
what  he  wants,  and  partly  does  not  want  what  he  knows."* 

§  10.  If  we  return  to  the  subject  of  the  syllogistic  logic,  we 
may  see  on  the  one  hand  that  its  moods  and  figures  will  not 
take  in  any  one  of  our  syntheses  except  the  synthesis  of  subject 
and  attribute.  The  fifth,  the  fourth,  the  third,  and  the  second, 
refuse  to  enter  the  traditional  limits.  On  the  other  hand  the 
first  of  our  syntheses  covers  every  argument  of  the  syllogistic 
logic.  An  inspection  of  the  figures  would  at  once  assure  us 
that  with  positive  reasoning  this  assertion  holds  good,  and  we 
must  now  proceed  to  test  our  conclusion  by  applying  it  to  the 
subject  of  negative  inference. 

*  Compare  on  the  subject  of  Casuistry  my  pamphlet,  Mr.  Sidgwick's 
Hedonism^  §  8,  and  Ethical  Studies^  pp.  142,  174,  foil. 


250  THE  PRINCIPLES   OF  LOGIC.  [Bk.  H.  Pt.  I. 


CHAPTER  V. 

NEGATIVE    REASONING. 

§  I.  The  general  nature  of  negative  reasoning  does  not 
vitally  differ  from  that  of  positive.  We  have,  given  us  in  the 
premises,  two  or  more  relations  presenting  us  with  certain 
identical  points,  and  on  the  basis  of  these  points  we  combine 
the  relations  into  an  individual  whole.  We  then  by  inspection 
find  a  new  relation  within  that  whole.  The  conclusion  may 
connect  two  terms  directly,  as  in  A  — B  — C  .'.  A  — C,  or  it 
may  connect  them  indirectly,  as  A  — B  — C  .'.  A  — (B)C,  or 
A(B)-C.  The  new  line  that  is  drawn  may  fall  clear  of  the 
middle-point  of  the  construction,  or  may  pass  through  it  on  the 
line  of  the  old  relations.  Negative  reasoning  and  positive  have 
all  these  qualities  in  common.  It  is  true  that  in  a  negative 
inference  the  line  that  connects  the  terms  of  one  relation  is  a 
line  of  denial ;  X)ne  part  of  the  figure,  which  ideally  we  con- 
struct, consists  of  a  repulsion  ;  and  the  fresh  connection  we  draw 
from  that  construction  is  a  connection  by  exclusion.  But  these 
differencee  are  varieties  within  the  same  main  principle. 

§  2.  It  might  seem  as  if  nothing  remained  for  us  to  do  but 
to  state  and  illustrate  those  negative  formulae  which  correspond 
to  the  axioms  of  affirmative  reasoning.  And  to  this  we  shall 
at  once  proceed  to  address  ourselves  ;  but  it  is  right  to  premise 
that  there  are  further  difficulties  which  lie  in  wait  for  us  at  the 
end  of  this  section.  • 

In  negative  reasoning  we  may  so  state  the  principle,  "  If  B 
is  related  within  one  genus  positively  to  A  and  negatively  to 
C,  then  A  and  C  are  negatively  related  within  that  genus. 
And  if  the  affirmative  and  negative  relations  (A  —  B,  B  —  C)  are 
heterogeneous,  yet,  if  one  is  in  the  category  of  subject  and 
attribute,  there  is  a  negative  inference  within  one  or  both  of 


Chap.  V.]  NEGATIVE   REASONING.  2$! 

the  two  categories  which  have  appeared  in  the  premises." 
Unless  A  —  B  B  —  C  are  within  the  same  genus,  or  unless  one  is 
a  relation  of  subject  and  attribute,  there  is  no  connection  at  all. 

I.  Synthesis  of  subject  and  attribute. 

{a)  Where  the  attribute  is  not  taken  as  distinct  from  every 
subject,  what  is  denied  of  the  attribute  is  denied  of  the  subject, 
and  where  the  attribute  is  denied  the  subject  is  denied. 

{b)  Where  the  subject  is  not  taken  as  distinct  from  every 
attribute,  what  is  denied  of  the  subject  is  denied  of  its  attri- 
butes, and  where  the  subject  is  denied  then,  in  that  sense,  the 
attribute  is  denied. 

{c)  Where  tw^o  subjects  have  the  same  or  a  different 
attribute,  they  are  so  far  not  different  or  not  the  same. 

Examples :  (a)  "  A  triangle  has  not  got  tw^o  right  angles  ; 
this  is  a  triangle,  and  has  therefore  not  two  right  angles."  "  A 
rectangular  triangle  is  not  equilateral ;  this  figure  is  equilateral, 
and  therefore  can  not  be  a  rectangular  triangle."  (b)  "  Man 
is  not  a  quadruped,  man  is  a  mammal,  therefore  a  mammal 
may  be  (the  human  mammal  is)  not  a  quadruped  ;  and  a 
quadruped  is  not  a  mammal  in  every  sense  of  that  adjective." 
(c)  "  My  horse  is  vertebrate,  this  animal  is  a  worm,  and  there- 
fore is  not  the  same  as  my  horse." 

II.  The  Synthesis  of  Identity  must  become  a  Synthesis  of 
Identity  and  Difference,  "  Where  two  terms  have  the  same 
point  in  common,  and  one  of  them  by  virtue  of  this  point  is 
different  from  a  third,  there  the  other  and  the  third  differ  in 
this  same  point." 

Example :  "  A  piano  (A)  is  in  tune  with  B,  which  is  not 
in  tune  with  C,  and  therefore  A  and  C  are  not  in  tune  with 
each  other." 

In  the  Synthesis  of  Degree,  of  Space,  and  of  Time,  we  have 
no  occasion  to  alter  the  formulae.     We  may  give  as  examples, 

III.  A  is  as  heavy  as  B,  B  is  not  lighter  than  C,  therefore 
A  is  not  lighter  than  C. 

IV.  A  is  not  before  B  in  time,  B  is  contemporary  with  C, 
therefore  A  is  not  before  C. 

V.  A  is  due  east  of  B,  C  is  not  north  of  B,  therefore  C  is 
not  north  of  A. 

§  3.  We  seem  to  have  performed  our  task  successfully, 


252  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  L 

but  must  deal  with  a  further  complication.  We  may  be  taken 
to  have  sinned  against  two  prominent  rules  of  the  traditional 
logic,  since  on  the  principles  we  have  given  you  may  get  a 
conclusion  from  two  negative  premises,  and  that  conclusion 
may  at  least  in  part  be  affirmative.  Yet  I  can  not  reject 
these  traditional  rules  as  errors,  and  if  they  have  committed 
oversights  is  a  question  which  turns  on  their  interpretation. 
Without  doubt  if  you  interpret  negative  premises  strictly,  that 
is,  take  them  in  the  shape  of  bare  denials,  then  the  rule  which 
forbids  an  inference  is  vaHd.  And  the  second  rule,  which 
confines  the  conclusion  to  a  mere  denial,  is  without  doubt  valid 
unless  you  break  through  another  syllogistic  precept.  If  you 
insist  on  eliding  the  middle  term,  then  not  only  must  the  result 
be  partly  negative,  but  it  really  is  limited  to  a  judgment 
which  denies.  And  thus,  if  in  their  statement  the  rules  turn 
out  to  have  gone  too  far,  they  at  all  events  have  been  based 
on  a  solid  foundation. 

It  is  not  hard  to  understand  this  ;  from  two  bare  denials 
there  can  come  no  conclusion,  because  there  can  not  be  any 
construction.  Why  no  construction  ?  Because  there  is  either 
no  common  point,  or,  if  there  is  a  common  point,  because  you 
do  not  know  the  position  of  the  other  terms.  Let  us  take  the 
last  first ;  in  negative  reasoning  we  may  represent  the  denials 
by  lines  of  exclusion  ;  but,  if  we  interpret  the  premises  strictly, 
we  find  ourselves  unable  to  give  these  lines  any  definite  position. 
A  is  not  C  nor  B,  but  the  exclusion  of  C  and  the  exclusion 
of  B,  though  we  represent  them  truly  by  lines  of  rejection,  fall 
we  know  not  where.  The  excluded  has  got  no  determinate 
position,  and  therefore  no  known  relation  to  other  elements. 

And  this  is  not  all,  for  if  we  wish  to  see  the  real  state  of 
the  case,  we  must  go  back  to  our  doctrine  of  the  negative 
judgment  (Bk.  I.  Chap.  III.).  A  mere  denial  does  not  in  any 
way  give  existence  or  position  to  the  thing  it  denies.  Thus 
in  "A  is  not  B"  we  assert  the  simple  rejection  of  B  by  an 
unstated  quality  belonging  to  A,  and  in  respect  of  B  we  know 
nothing  at  all  but  its  banishment  from  our  universe.  But  it  is 
obvious  that,  when  a  term  is  so  banished,  we  know  about  it 
nothing  definite  save  its  rejection  by  A. )  No  matter  then  how 
many  negative  premises  we  may  have,  since  by  adding  to  the 


Chap.  V.]  NEGATIVE  REASONING.  253 

number  of  our  banished  terms  we  do  not  get  any  nearer  a 
conclusion.  The  exiles  do  not  move  in  any  real  world  at  all, 
and  to  unite  them  by  a  line  of  connection  is  impossible. 

Thus  even  if  two  denials  have  a  common  subject,  we 
can  not  go  from  those  denials  to  a  further  relation.*  And  we 
are  stopped  elsewhere  by  another  obstacle,  for  we  have  not 
got  the  common  centre  required  for  a  construction.  In  "  A  is 
not  B  and  B  is  not  C,"  we  have  in  the  one  case  the  exclusion 
of  B,  and  in  the  other  case  the  exclusion  byYi\  we  have  first 
absence  and  then  presence.  And  again,  if  we  give  our  premises 
another  form  and  say  "  B  is  not  A  and  B  is  not  C,"  we  can  not 
go  to  a  relation  between  A  and  C,  since  (apart  from  other 
reasons)  the  quality  of  B  may  be  quite  different  in  each  denial. 
Perhaps  from  "  C  is  not  A  and  B  is  not  A"  we  might  be 
tempted  to  argue  to  a  positive  relation  of  partial  identity 
between  C  and  B.  But  here  again  our  centre  would  be 
wanting,  for  we  do  not  know  if  the  quality  which  ensures  the 
rejection  is  not  wholly  different  in  each  of  these  cases.  And 
thus  our  premises  may  furnish  a  ground  for  suspicion,  but  they 
no  more  give  us  proof  than  would  such  positive  premises  as 
"  A  is  like  B  and  C,"  or  "A  is  like  B,  and  B  is  like  C."  In 
short  given  two  denials  there  is  either  no  common  point,  or 
else  the  two  relations  which  start  from  that  centre  terminate 
in  nothing  which  can  be  related. 

The  rule  which  forbids  all  the  premises  to  deny  is  thus 
shown  to  have  a  solid  foundation  ;  and  we  may  say  the  same 
of  the  rule  which  prohibits  a  positive  conclusion.  For  since 
the  predicate  denied  is  completely  expelled  from  the  world  of 
the  subject,  we  are  left  with  no  relation  beside  the  repulsion. 
It  is  clear  then  that  you  can  not  have  a  positive  connection 
either  between  the  predicate  and  that  which  exists  in  friend- 
ship with  the  subject,  or  between  the  subject  and  what  shares 
the  fortunes  of  the  predicate.  In  "A-B  B  —  C,"  if  one 
relation  is  negative,  we  can  not  in  any  way  draw  a  line  A  —  C 
which  falls  outside  B.  For  A  and  C  will  be  separated  in 
two  different  worlds,  and  if  one  is  in  any  way  to  come  in 

*  In  "  A  is  not  B  and  not  C,  therefore  B  and  C  are  so  far  alike  "  the 
premises  are  positive.  B  and  C  are  both  disparate  in  quality  with  A, 
or  have  the  psychical  fact  of  rejection  in  common. 


254  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  L 

contact  with  the  other,  the  line  of  connection  must  pass 
through  B.  But  on  one  side  of  B  is  a  mere  rejection,  and  it  is 
therefore  evident  that  a  positive  line  can  not  be  drawn  beyond 
the  centre,  and  that  the  new  relation  must  add  to  the  rejection 
which  already  exists  in  B.  It  is  indeed  not  true  that  this 
extension  is  a  mere  denial,  and  again  it  is  not  true  that  the 
conclusion  must  be  wholly  negative  ;  but  for  all  that  the  second 
traditional  rule  has,  like  the  first,  a  rational  foundation. 

§  4.  But  though  both  the  precepts  stand  on  a  solid  basis, 
the  meaning  of  the  first  calls  for  some  restriction,  and  the 
second  is  not  true  without  an  exception.  Two  denials  should 
not  give  a  conclusion  at  all,  and  yet  you  can  not  say  that  of 
two  premises  which  deny.  In  his  Principles  of  Science^  p.  6^, 
Prof.  Jevons  has  called  attention  to  the  subject  ; 

"  Whatever  is  not  metallic  is   not   capable  of   powerful  magnetic 

influence,  (1) 
Carbon  is  not  metallic,  (2) 
Therefore,  carbon  is  not  capable  of  powerful  magnetic  influence  (3)." 

This  argument  no  doubt  has  quaternio  termijtorum  and  is 
vicious  technically,  but  the  fact  remains  that  from  two  denials 
you  somehow  have  proved  a  further  denial.  "  A  is  not  B, 
what  is  not  B  is  not  C,  therefore  A  is  not  C  ; "  the  premises 
are  surely  negative  to  start  with,  and  it  appears  pedantic  either 
to  urge  on  one  side  that  "  A  is  not-B  "  is  simply  positive,  or 
on  the  other  that  B  and  not-B  afford  no  junction.  If  from 
negative  premises  I  can  get  my  conclusion,  it  seems  idle  to 
object  that  I  have  first  transformed  one  premise  ;  for  that 
objection  does  not  show  that  the  premises  are  not  negative, 
and  it  does  not  show  that  I  have  failed  to  get  my  conclusion. 

And  if  we  leave  the  limits  of  the  syllogistic  logic  exaniples 
come  to  us  from  every  side  ;  "  A  degree  A  can  not  be  less 
than  B,  B  is  not  less  than  C,  therefore  C  can  not  be  greater 
than  A,  or  A  must  be  equal  to  or  greater  than  C  ; "  "  Event 
A  is  not  before  B,  C  is  not  after  B,  therefore  A  is  not  before 
C,  or  C  is  simultaneous  with  A  or  before  it ; "  "  C  is  not 
north  of  B,  B  is  not  north  of  A,  therefore  A  is  not  south  of  C, 
or  A  is  due  east,  or  west,  or  on  the  north  side  of  C."  It  is 
bootless  here  to  fall  doggedly  back  on  the  technical  rules  of 
mood  and  figure,  since,  if  we  keep  to  these,  we  can  not  even 


Chap.  V.]  NEGATIVE  REASONING.  255 

prove  the  positive  conclusions  from  the  positive  premises.  If 
"  A  to  right  of  B  "  is  a  positive  relation  of  A  to  B  which  can 
not  be  reduced  to  predicate  and  copula,  why  should  we  not 
have  in  "  A  not  to  right  of  B "  a  negative  relation  which  is 
also  irreducible  ?  The  traditional  logic  may  object  to  the 
latter,  but  it  has  put  itself  out  of  court  by  first  objecting  to 
the  former ;  and,  if  it  is  quite  wj-ong  in  one  case,  it  may  be 
quite  wrong  in  another. 

§  5.  In  this  case  it  is  not  wrong,  for  it  happens  to  be  right. 
The  restricted  portion  of  the  field  it  occupies  happens  here  to 
be  the  limit  of  the  subject.  For  denial  as  such  can  not  fall 
outside  the  single  category  in  which  the  syllogism  is  shut  up. 
A  denial  as  such,  we  have  seen  long  ago,  is  merely  the 
exclusion  of  an  ideal  suggestion,  and  hence  no  negative  rela- 
tion between  positive  existences  can  ever  be  expressed  by  a 
mere  denial.  But  then  on  the  other  hand  a  bare  denial  can 
never  be  found,  for,  when  A  excludes  some  relation  to  B 
which  is  offered  in  idea,  there  must  always  be  a  ground  for 
that  rejection.  The  base  of  the  rejection  must  be  a  positive 
quality,  unspecified  but  necessary  ;  and  hence,  wherever  we 
have  negative  judgment,  we  have  in  addition  some  positive 
assertion,  which  may  not  be  explicit  but  which  must  be  there. 
And  this,  as  we  saw,  is  such  a  fount  of  ambiguity  that  in 
denials  we  seldom  know  all  we  are  saying  (p.  120). 

We  may  verify  this  in  the  examples  we  have  used.  In  the 
first  we  assume  that  A  has  degree,  and  upon  that  basis  of 
positive  assertion  we  proceed,  by  exclusion  of  the  alternatives 
denied,  to  a  positive  result.  In  the  second  the  argument 
really  starts  from  "  A  is  an  event  with  a  position  in  the  series 
after  or  simultaneous  with  B."  In  the  third  we  assume  that  A 
falls  in  space  and  in  a  relation  to  B  marked  out  by  exclusion. 
In  all  these  if  we  kept  to  mere  denial  we  could  not  prove 
anything,  since  we  may  deny  "  less  than  B,"  or  "  prior  to  B,"  or 
"  north  of  B,"  of  what  has  no  degree  and  no  time  and  no 
position.  Such  a  course  might  be  unusual  but  is  legitimate  and 
recognized,  because  the  denial  as  such  covers  all  possibilities. 

§  6.  If  we  take  as  our  rule  that  from  negative  premises  you 
can  not  argue,  then,  stated  so,  that  rule  is  incorrect ;  and  it  is 
false  even  to  say  that  denials  give  no  inference,  since  every 


256  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  L 

denial  has  a  positive  side.  That  positive  side  is  latent  and 
may  escape  us ;  in  "  7  is  not  less  than  5  -f-  i,  5  +  i  is  not  less 
than  4,  and  therefore  7  is  not  less  than  4,"  we  do  not  say  that 
7  is  a  number  at  all  and  must  stand  in  some  numerical 
relation  with  5  +  1.  And  thus  in  assuming  it  we  have  passed 
beyond  the  denial,  though  not  beyond  what  the  denial 
implies.  It  is  necessary  therefore  in  expressing  our  rule  to 
make  a  distinction.  You  can  not  argue,  we  must  say,  from 
two  denials,  so  long  as  you  keep  to  bare  denial.  If  you 
treat  the  assertion  which  those  denials  imply,  then  you  are 
not  keeping  to  the  side  of  denial.  And,  if  we  formulate  it  so, 
the  rule  will  hold  good. 

Denial  implies  removal  or  exclusion,  and  from  exclusions 
or  removals  you  can  get  a  conclusion.  "  Removal  of  A  is 
removal  of  B,  removal  of  B  is  removal  of  C,"  gives  "  Removal 
of  A  is  removal  of  C  ;  "  and  "  Absence  of  A  is  absence  of  B, 
absence  of  B  is  absence  of  C,"  proves  that  absence  of  A  is 
absence  of  C.  But  here  our  real  premises  are  "  What  removes 
A  removes  B,"  and  "  That  which  is  without  A  is  also  without  B." 
You  can  hardly  say  that  these  premises  are  quite  positive, 
but  they  contain  much  more  than  a  bare  denial.  Thus 
negation  must  always  remain  ambiguous  (Book  I.  Chap.  III.), 
for  "  No  A  is  B,"  may  merely  banish  B,  while  again  it  may 
assert  "  The  absence  of  A  is  the  presence  of  B."  "  If  A  is 
there  then  B  will  not  be  there,"  and  "  Since  A  is  not  there  B 
must  be  there "  are  both  expressed  by  this  doubtful  formula. 
But  if  we  confine  negation  to  mere  denial  it  is  the  exclusion 
of  an  idea  by  an  unspecified  quality,  and  if  we  confine  the 
denial  to  its  negative  side  it  is  the  mere  exclusion  of  a 
suggested  idea.  It  is  upon  this  last  understanding  that  the 
traditional  rule  is  actually  valid. 

It  would  not  be  valid  if  negation  were  assertion.  If  in  "  A 
is  not  B  "  the  exclusion  of  B  were  a  condition  necessary  to 
the  existence  of  A,  then  B  must  be  banished  if  A  is  to  be 
there,  and  if  B  is  not  there  B  can  not  be  banished.  And  from 
negative  premises,  if  so  interpreted,  it  no  doubt  might  be 
possible  to  get  some  conclusion.  But  this  interpretation  we 
long  ago  saw  was  erroneous.  The  denial  excludes  an  ideal 
suggestion,  and  the  fact  which  lies  at  the  base  of  the  exclusion 


Chap.  V.]  NEGATIVE   REASONING.  2^"/ 

need  be  no  relation  of  A  to  B,  but  on  the  other  hand  a  quality 
of  A  or  again  of  some  more  ultimate  reality.  But  this 
quality  is  latent  and  wholly  unspecified. 

§  7.  We  have  seen  that,  upon  a  strict  interpretation  of 
negative  premises,  the  first  of  the  rules  we  mentioned  is  valid. 
What  then  is  to  become  of  our  principles  of  synthesis,  since 
they  collide  with  the  rule  and  can  not  be  true  ?  But  I  think  it 
is  better  to  leave  them  standing,  for  they  are  valid  if  the 
sense  of  negative  premises  is  not  confined  to  what  they  deny. 

Otherwise  of  course  they  must  be  corrected.  It  is  im- 
possible to  have  any  negative  inference  which  will  fall  wholly 
within  the  categories  of  identity,  or  time,  or  space,  or  again 
degree.  One  premise  at  least  must  confine  itself  to  the 
relation  of  subject  and  attribute. 

This  is  very  obvious.  One  premise  must  deny,  and  no 
denial  as  such  can  be  referred  to  any  category  beyond  the 
relation  of  attribute  to  subject.  The  denial  is  the  exclusion 
of  an  ideal  suggestion,  and  a  relation  of  time,  or  space,  or 
degree  falls  within  this  suggestion  which  the  subject  repels. 
It  is  clear  then  that  the  denial  of  a  connection,  say  of  space, 
is  not  a  connection  in  the  category  of  space.  The  subject 
excludes,  it  is  true,  by  a  quality,  but  you  do  not  know  what 
that  quality  is.  And  since  you  do  not  know  what  quality 
repels,  the  repulsion  and  the  quality  which  forms  its  basis  can 
not  pass  beyond  the  sphere  of  simple  attribution.  Thus  "  A 
is  not  north  of  B,"  if  restricted  to  denial,  means  "  A  repels  the 
suggestion  A  to  north  ofB;"  and  we  can  not  possibly  take 
this  as  anything  more  than  an  adjective  of  A. 

If  we  refer  to  the  examples  we  gave  in  illustration  (§  2),  we 
must  so  interpret  the  negative  premises.  "  B  is  not  in  tune 
with  C  "  means  "  B  excludes  the  attribute  of  being  in  tune 
with  C,"  and  "  B  is  not  lighter  than  C  "  means  "  B  excludes  a 
certain  relation  of  degree  to  C."  But  of  course  B  might  repel 
these  relations  with  C  although  it  possessed  no  note  at  all, 
and  although  it  had  no  degree  of  any  kind  ;  and  in  the  same 
way  the  denial  that  B  is  in  such  a  position  may  be  true 
though  B  has  no  place  whatever.  If  one  of  the  premises  be 
confined  to  denial  that  premise  is  shut  up  within  the  category 
of  subject  and  attribute. 

S 


258  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  L 

But  having  so  restricted  the  character  of  our  premises  it  is 
natural  to  expect  a  restricted  result.  Our  rule  will  now  be, 
"  In  all  negative  inferences  the  conclusion  is  confined  within  the 
relation  of  subject  and  attribute,  unless  that  conclusion  can  in 
any  way  be  affirmative.'' 

§  8.  But  can  the  conclusion  be  anything  but  negative  ? 
This  is  the  question  we  have  next  to  discuss.  The  rule 
forbade  an  affirmative  result,  and  we  saw  that  this  rule  was 
based  upon  truth.  For  since  in  A  —  B  B  —  C  one  relation  is 
negative.  A  — C  can  not  be  joined  by  a  line  of  connection 
which  passes  anywhere  except  through  B.  And,  since  part 
of  this  line  must  consist  of  an  exclusion,  we  saw  that  A  —  C 
must  have  a  negative  character  (§  3). 

The  result  is  unshaken,  but  it  omits  a  possibility.  The 
conclusion  need  not  take  the  form  of  A  —  C,  since  the  result 
which  we  get  from  the  union  of  our  premises,  may  be  found  in 
the  whole  ideal  construction.  The  syllogistic  practice  is  to 
elide  the  middle ;  but  if  we  do  not  choose  to  perform  this 
elision,  who  on  the  one  hand  can  order  us  to  do  so  ?  And  on 
the  other  hand  who  can  deny  that  the  result  which  we  obtain 
is  a  real  inference ?  "A  takes  precedence  of  (is  lighter  than, 
sits  on  the  right  of)  B,  B  is  not  younger  than  C,  therefore  A 
takes  precedence  of  (is  lighter  than,  sits  on  the  right  of)  a 
person  (B)  not  younger  than  himself."  There  is  here  no 
direct  conclusion  A  —  C,  and  there  is  again  no  inference  within 
one  category,  and  at  the  same  time  one  premise  seems  to  be 
used  as  mere  denial.  On  the  other  hand  I  see  no  reasonable 
ground  on  which  we  can  deny  that  we  have  got  a  conclusion. 
Yet  this  conclusion  is  neither  a  mere  denial,  nor  does  it  fall 
within  the  category  of  subject  and  attribute. 

We  may  go  beyond  this.  In  the  syllogism  itself,  if  we 
decline  to  elide  the  middle  term  B,  we  may  have  an  inference 
the  conclusion  of  which  is  more  than  a  denial.  Take  an 
instance  in  Celarent,  "  A  lung-breathing  animal  (B)  is  not  a  fish 
(C).  All  Cetacea  (A)  breathe  by  means  of  lungs  (B)."  From 
this  the  regular  conclusion  is  "  A  is  not  C."  But  "All  Cetacea 
have  a  quality,  viz.  breathing  through  lungs,  which  excludes 
the  assertion  that  any  are  fish,"  will  surely  come  without  flaw 
from  the  premises.     It  certainly  is  more  than  a  bare  denial. 


Chap.  V.]  NEGATIVE  REASONING.  259 

and  it  is  no  mere  repetition  of  the  premises.  And  to  say,  If 
A  does  not  exclude  C  after  the  middle  has  been  elided,  there 
shall  be  no  inference  and  there  can  be  no  conclusion,  seems 
purely  arbitrary.  Nor  indeed  do  I  see  how  this  insistance  on 
elision,  if  we  pressed  it  to  its  consequences,  would  prove  com- 
patible with  the  general  validity  of  the  third  figure. 

§  9.  The  result  we  are  left  with  may  thus  be  stated.  From 
two  denials  there  is  na  conclusion.  If  one  premise  denies  and 
keeps  to  denial,  then  one  premise  at  least  is  limited  to  the 
genus  of  subject  and  attribute.  If  the  middle  term  B  falls  out 
of  the  conclusion,  if  A  and  C  are  connected  through  B,  but 
not  by  means  of  an  intermediate  B,  then  the  conclusion  denies 
and  falls  also  within  the  above-named  gemis.  But  if  B  is  kept 
standing,  the  conclusion  may  at  least  in  part  be  positive, 
and  is  not  confined  to  a  single  category. 

The  general  formula  for  negative  reasoning,  if  we  confine 
ourselves  to  the  side  of  bare  denial,  may  be  stated  as  follows  : 
If  B  repels  a  content  C,  and  is  in  relation  with  a  third  term  A, 
then  A  and  C  will  either  be  related  directly  by  way  of  denial 
or  else  will  be  elements  in  a  whole  A  —  B  —  C,  of  which  at  least 
one  member  will  be  confined  to  the  genus  of  subject  and 
attribute.  And  I  think  with  this  we  may  take  leave  of  a  subject 
which  has  proved  perhaps  more  troublesome  than  interesting. 


S   2 


260  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Ft.  L 


CHAPPER  VI. 

TWO   CONDITIONS   OF  INFERENCE. 

§  I .  We  may  briefly  recapitulate  the  result  we  have  reached. 
An  inference  is  always  an  ideal  construction  resultingjn  the 
perception  of  a  new^connection.  So  far  as  this  perception  of 
the'cohclusion  is  concerned,  there  is  no  possibility  of  laying 
down  rules,  and  the  syllogistic  logic  teaches  a  superstition. 
That  logic  again  has  failed  to  include  all  the  principles  of  syn- 
thesis which  operate  in  construction,  and  it  is  falsely  confined 
to  a  single  category.  It  is  wrong  again  as  to  the  number  of 
the  premises ;  and  in  insisting  on  the  necessity  of  a  major 
premise,  it  is  clinging  blindly  to  exploded  metaphysics  in  direct 
defiance  of  the  most  palpable  facts.  And  it  makes  a  further 
mistake  as  to  the  necessity  of  elision. 

It  might  seem  that  having  thus  rejected  the  syllogism  we 
must  throw  in  our  lot  with  its  hereditary  enemies.  But  yet, 
if  the  friends  of  the  syllogism  will  allow  it,  we  would  rather 
take  a  place  on  their  side.  Our  differences  are  trivial  compared 
with  our  agreements,  and  as  against  the  enemy  our  cause  is  the 
same,  for  we  have  in  common  these  two  beliefs  :  (i)  It  is 
impossible  to  reason  except  upon  the  basis  of  identity,  (ii)  It 
is  impossible  to  reason  unless  at  least  one  premise  is  universal. 
It  will  be  time  to  say  vicerunt  empirici  when  these  positions 
have  both  been  forced. 

§  2.  (i)  I  will  begin  with  the  necessity  of  an  identical 
point.  We  know  that  an  inference  is  an  ideal  construction, 
and  the  reality  of  this  construction  depends  on  its  unity ;  if 
the  construction  is  not  individual  it  is  merely  fictitious.  But 
how  can  any  construction  have  unity  unless  it  is  united  by 
a  common  point.?  And  how  can  any  point  be  common, 
unless  in  both  the  premises  it  is  one  and  the  same  } 

It  is  obvious  that  suppose  the  problem  before  us  is  to  find 


Chap.  VI.]  TWO   CONDITIONS   OF   INFERENCE.  261 

the  relation  of  S  to  P  by  means  of  their  common  relation  to  M, 
and  if,  by  the  hypothesis,  S  —  M  and  M  —  P  must  be  given 
separately,  an  advance  is  impossible,  unless  in  both  premises 
M  is  the  same.  Given  S  — M^  &  M^  — Pyou  can  make  no 
construction,  for  you  have  no  bridge  to  carry  you  over  from 
M^  to  M^.  The  back  of  your  inference  now  is  broken  and  the 
extremities  no  longer  belong  to  any  individual  principle. 
Unless  M  in  both  cases  is  absolutely  the  same  you  can  not 
inter-relate  S  and  P. 

If  we  are  willing  to  give  up  the  superstition  of  the  copula 
and  to  admit  a  diversity  of  relations  in  judgment,  we  may  say 
that  in  inference  every  pair  of  premises  has  one  term  the  same, 
and  that,  if  it  is  not  the  same,  there  can  be  no  inference. 

§  3.  It  is  obvious,  if  we  dismiss  our  hardened  prejudices  and 
consider  the  question  fairly  by  itself,  that  you  can  not  argue  on 
the  strength  of  mere  likeness.  Whatever  else  may  be  right  this 
at  all  events  must  be  wrong ;  "  A  is  similar  to  B,  and  B  to  C, 
and  therefore  A  is  like  C,"  is  a  vicious  inference,  one  that  need 
not  always  be  mistaken  in  fact,  but  that  always  must  be  a  logical 
error.  In  practice  I  think  we  should  all  admit  this.  An 
inference  based  on  nothing  but  likeness  is  utterly  invalid  ;  it  is 
certainly  ambiguous  and  probably  false. 

Likeness  and  sameness  should  never  be  confused,  for  the 
former  refers  properly  to  a  general  impression.  Similarity  is 
a  perceived  relation  between  two  terms  which  implies  and 
rests  upon  a  partial  identity.  If  we  say  that  A  and  B  are 
alike,  we  must  be  taken  to  assert  that  they  have  something  the 
same.  But  we  do  not  specify  this  point  of  sameness,  and  the 
moment  we  do  that  we  have  gone  beyond  mere  similarity.  If 
A  and  B  for  instance  both  have  lungs  or  gills  they  are  so 
far  the  same,  and,  on  the  strength  of  and  because  of  this  partial 
identity,  they  may  present  themselves  to  us  as  generally 
similar.  But  now  add  to  these  the  further  statement  "  B  and 
C  are  alike."  If  we  reduce  the  likeness  here  to  partial 
identity  we  may  find  that  the  common  point  is  here  once  again 
the  possession  of  lungs  or  gills,  and  on  the  strength  of  this  we 
may  go  on  to  argue  that  A  and  C  (the  extremes)  are  alike. 
But  what  actually  inter-relates  A  and  C  is  not  general 
similarity  at  all.     If  all  you  knew  was  that  B  was  like  C,  the 


262  THE   PRINCIPLES  OF   LOGIC.  [Bk.  IL  Ft.  L 

point  of  identity  would  be  quite  unspecified,  and  the  fact 
might  be,  not  that  both  had  lungs  or  gills,  but  that  each  had 
one  eye  or  the  freedom  of  the  will.  In  this  case  though  each 
pair  has  its  own  internal  likeness,  you  could  not  infer  the 
similarity  of  A  to  C. 

And  if  in  answer  I  am  told  that  this  is  irrelevant,  and  that 
it  does  not  apply  where  the  likeness  is  exact,  I  can  only  reply 
that  I  am  waiting,  and  have  been  waiting  for  years,  to  be  told 
what  is  meant  by  an  "exact  likeness."  "A  and  B  are  not  the 
same,  but  they  are  exactly  alike,  and  therefore  whatever  is 
true  of  B  must  be  true  of  A."  But  what  can  this  mean  >  In 
the  case  of  some  twins  it  might  be  right  to  punish  one  for  the 
other,  and  we  should  no  longer  care  to  identify  criminals. 
If  a  picture  is  "  exactly  like  "  a  person,  then  if  one  is  not  dead 
the  other  will  be  alive.  If  a  cast  is  "  exactly  like  "  an  original 
I  suppose  the  same  thing  will  be  in  two  places  at  once ;  and  it 
is  no  mere  metaphor  if  in  certain  cases  the  father  is  said  to 
survive  in  his  children,  though  the  children  might  then  cease 
to  survive  the  father.  But  it  is  idle  to  pursue  these  frivolous 
consequences;  the  meaning  which  "  exactly  like  "  carries  to 
my  mind  is  nothing  whatever  but  "partially  the  same"  or 
"identical  in  some  point  or  points."  Likeness  is  always  a 
perceived  relation  based  upon  a  partial  identity.  In  mere 
general  similarity  the  identity  will  be  indefinite,  where  the 
likeness  is  more  special  it  must  at  least  be  partly  defined, 
and  where  the  similarity  is  called  "  exact "  I  understand  that 
there  is  a  definite  point  or  points,  in  respect  of  which  the  same- 
ness is  complete.  And  if  likeness  did  not  imply  identity  all 
inference  based  upon  it  would  be  vicious.  In  practice  every 
one  would  allow  it  to  be  vicious,  nor  do  I  understand  how  in 
theory  it  is  possible  to  take  it  as  having  any  other  tharacter. 

I  am  most  anxious  to  enter  into  (if  I  can),  and  to  discuss 
the  meaning  our  "  advanced  thinkers  "  may  have  attached  to 
"likeness"  or  "similarity."  But  I  am  forced  to  say  again  in 
this  place  what  I  had  to  say  elsewhere  some  years  ago.* 
While  our  "advanced  thinkers"  merely  sing  the  old  song 
which  they  have  learnt  and  which  their  fathers  have  taught 
them,  they  can  hardly  expect  to  have  its  meaning  discussed, 
*  Ethical  Studies^  p.  151. 


Chap.  YL]  TWO   CONDITIONS   OF   INFERENCE.  263 

nor  can  they  complain  if  they  are  treated  as  having  no  real 
meaning. 

§  4.  A  construction  of  given  premises  is  not  possible  unless 
each  pair  of  premises  has  a  common  point.  And  this 
common  point  must  be  an  identical  term.  Thus  in  "A  — B 
B-C  therefore  A-B~C,"  the  B  in  each  premise  must  not 
be  merely  alike,  but  must  be  absolutely  the  same.  But  here, 
after  having  avoided  one  error,  we  are  threatened  by  another 
and  opposite  mistake.  For  if  it  is  wrong  to  say  that  B  is  not 
the  same,  it  is  equally  wrong  to  deny  that  it  is  different. 

This  may  look  mysterious  but  is  really  quite  simple.  If 
B  in  both  premises  were  so  far  the  same  that  no  difference  of 
any  kind  belonged  to  it,  then  it  is  obvious  at  once  that  both 
premises  must  be  identical,  or  else  that  their  differences  do 
not  concern  B.  But  in  each  of  these  cases  the  inference 
disappears.  If  the  premises  are  the  same  their  repetition  is 
meaningless,  and  if  the  differences  they  contain  are  indifferent 
to  B  it  is  clear  that  no  construction  can  be  made,  since,  if  B  is 
the  centre,  it  carries  no  radii  and  has  no  circumference.  An 
identity  which  is  not  a  synthesis  of  differences  is  plainly  inert 
and  utterly  useless. 

B  is  the  same  amid  difference,  and  though  different  is  the 
same,  for  it  is  an  ideal  content,  the  product  of  abstraction, 
appearing  in  and  differenced  by  two  several  contexts.  So  far 
as  it  is  the  one  content  B,  so  far  it  is  absolutely  and  entirely 
the  same  ;  so  far  as  it  is  a  member  of  diverse  connections,  so 
far  it  carries  with  it  a  difference.  And  the  process  of  inference 
depends  entirely  on  this  double  aspect ;  for  it  is  because  B  is 
different  and  yet  the  same,  that  its  differences  are  able  to  be 
interrelated.  If  it  were  not  different  it  would  have  nothing 
to  connect,  and  if  it  were  not  the  same  there  could  be  no 
connection.  Inference  rests  upon  the  assumption  that,  if  the 
ideal  content  is  the  same,  then  its  differences  will  be  the  radii 
of  one  centre.  In  other  words  if  B  is  the  same,  what  is  true 
of  it  in  one  context  is  true  of  it  in  afiother. 

§  5.  We  have  returned  to  what  we*  called  the  Principle  of 
Identity  (Book  I.  Chap.  V.).  We  might  call  it  again  the 
Axiom  of  the  Identity  of  Indiscernibles,  and  we  can  put  the 
thing  in  more  simple  language  if  we  say  that  inference  rests 


264  '  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  L 

on  the  principle  that  what  seems  the  same  is  the  same,  and 
can  not  be  made  different  by.  any  diversity,  and  that  so  long  as 
an  ideal  content  is  identical  no  change  of  context  can  destroy 
its  unity.  The  assumption  in  this  principle  may  be  decried  as 
monstrous,  and  I  do  not  deny  that  perhaps  it  is  false.  In  a 
metaphysical  work  this  question  would  press  on  us,  but  in 
logic  we  are  not  obliged  to  discuss  it  (Book  III,  Part  II. 
Chap.  IV.).  The  axiom  may  be  monstrous  or  again  it  may 
be  true,  but  at  least  one  thing  is  beyond  all  doubt,  that  it  is 
the  indispensable  basis  of  reasoning.  It  may  be  false 
metaphysically,  but  there  is  no  single  inference  you  possibly 
can  make  but  assumes  its  validity  at  every  step. 

§  6.  It  is  easy  to  misunderstand  it,  and  it  is  sure  to  be 
misunderstood.  I  shall  be  told  that  spaces  and  times  are 
indiscernible  and  yet  are  not  identical.  But  this  objection 
rests  on  a  complete  mistake.  As  spaces  or  times  of  a  certain 
character  A  and  B  surely  are  identical ;  as  different  elements 
within  the  same  series  A  and  B  are  surely  not  indiscernible. 
It  is  one ,  superstition  to  think  you  have  relations  whose 
terminal   points   are   nothing  beyond    the   relation.*      It   is 

*  I  am  prepared  to  go  a  good  deal  beyond  this.  If  occasion  offered  I 
should  be  ready  to  argue  that  you  can  not  have  a  relation  between  points 
that  are  not  different  in  quahty.  Not  only,  for  instance,  must  spaces 
related  be  more  than  a  mere  relation  in  space,  but  they  must  also  have  a 
difference  in  quality.  It  is  not  possible  to  contemplate  points  in  relation 
unless  you  distinguish  them  by  a  qualitative  reference  to  the  right  or  left 
or  upper  or  lower  sides  of  your  body,  and  the  different  sensations  which 
are  at  the  root  of  these  divisions,  or  again  unless,  by  a  qualitative  mark 
such  as  A  or  B,  you  choose  to  make  one  different  from  the  other.  It 
may  be  objected  that  in  certain  cases  the  difference  of  quality  is  only  one 
aspect  of  the  whole  relation.  This  view  at  least  recognizes  the  existence 
of  the  difference,  and  I  will  not  here  discuss  it.  The  ultimate  connection 
of  quality  and  relation  is  a  most  difficult  problem.  But  it  is  clear  that 
taken  in  their  phenomenal  appearance  the  one  can  not  be  reduced  to  the 
other.  Is  this  double  aspect  true  of  the  reality  ?  Has  that,  as  we  are 
forced  in  the  end  to  apprehend  ^it,  a  single  nature  which  combines  two 
sides,  and  is  so  the  root  of  the  double  appearance  ?  Can  we  suppose  that 
qualities  are  generated  by  the  strife  of  some  counterpart  of  what  appears 
to  us  as  relations  ?  Or  is  it  true  that  supersensible  qualities  are  the 
reality  which  we  perceive  as  phenomenal  relations  ?  Or  is  the  question 
unanswerable  ?  If  it  is,  we  at  least  must  not  do  violence  to  the  given  on 
the  strength  of  a  theory  which  we  can  not  defend  (cf.  Book  I.  Chap.  II. 
§  65  foil.). 


Chap.  YL]  TWO   CONDITIONS   OF   INFERENCE.  265 

another  superstition  to  fancy  relations  as  an  arbitrary  network 
stuck  on  from  the  outside  by  destiny  or  chance,  and  making 
no  reasonable  difference  to  anything.  And  the  root  of  both 
superstitions  is  the  same.  It  is  the  refusal  to  recognize  that 
the  content  of  the  given  has  always  two  sides,  sensible 
qualities  and  relations,  and  that  one  side  can  never,  except 
by  an  artifice,  be  separate  from  or  merged  in  the  other.  I 
do  not  say  that  these  two  elements  are  metaphysically 
irreducible ;  I  do  say  that,  taking  them  each  as  it  stands,  you 
must  treat  them  each  as  a  character  of  the  given.  It  is  a  dire 
illusion  to  take  the  content  of  the  given  as  either  qualities 
without  relation  or  relations  without  qualities,  or  to  treat  the 
one  side  as  external  to  the  other.  Both  are  given  together 
and  given  within  the  content.  It  was  shown  above  (Bk.  I. 
Chap.  11.  §  21)  that^pace  and  time-relations  are  wo principium 
individuatio7iis ;  for  they  fall  within  the  what^  and  do  not 
make  the  this, 

And  another  result  was  brought  out  in  that  Chapter. 
Unless  judgments  of  sense  make  a  false  assertion  they  affirm 
or  deny  connections  of  content,  and  they  do  not  affirm 
anything  else  whatever.  It  is  absurd  to  object  that  if  Caesar 
is  the  same,  he  is  in  Gaul  and  in  Italy,  two  places  at  once,  or 
that  if  he  is  thirty  he  is  also  twenty-nine.  The  "  at  once " 
and  the  "  also  "  conceal  the  old  error.  Of  course  it  is  not  true 
that  the  identical  Caesar  under  the  same  conditions  can  be 
differently  related  to  Italy  in  space  or  to  his  own  birth  in 
time  ;  but  then  surely  the  conditions  vary  indefinitely.  The 
mere  lumping  together  unspecified  conditions  under  the  head 
"  is  now  "  does  not  show  that  the  conditions  are  indiscernible, 
and  that  striking  the  differences  out  of  the  account  we  are 
forced  to  predicate  contradictions  of  Csesar.  What  is  true  of 
Caesar  in  a  certain  context  is  true  of  the  same  Caesar  in  any 
other  context.  But  this  does  not  mean  that  one  context  is 
the  other  or  is  to  be  confused  with  the  other.  It  means  that 
Caesar  has  two  different  contexts,  and  that  the  truth  of  one 
can  be  no  reason  whatever  for  the  falsehood  of  the  other.  If 
we  fancy  this  is  so  we  have  given  to  one  or  to  both  assertions 
a  meaning  which  is  false,  and  we  must  be  sent  back  once 
more  to  study  the  discussions  of  Book  I.  Chapter  II. 


266  THE   PRINCIPLES   OF  LOGIC.  [Bk.  II.  Pt.  1. 

§  7.  And  there  is  another  misunderstanding  against  which 
we  must  guard.  That  what  is  true  of  B  here  is  true  of  B 
everywhere,  means  that,  wherever  B  happens  to  be,  you  can 
say  of  it  always  what  you  have  said  of  it  once.  This  B  you 
assert  of  is  the  self-same  B  that  appears  in  the  differences,  but 
it  is  not  the  B  just  as  it  appears  in  those  differences.  In 
A  —  B,  B  —  C,  the  B  is  identical  and  A  and  C  are  connected  by 
that  identity.  But  A  and  C  are  not  themselves  identical,  and 
you  can  not  predicate  B  —  C  of  A  —  B.  The  B,  of  which  what 
has  once  been  said  holds  good  for  ever,  is  not  the  B  which  is 
one  thing  with  A  or  one  thing  with  C.  It  is  the  abstraction, 
the  idealized  content  B,  which  is  different  from  its  contexts 
and  yet  connected  with  them  and  on  the  strength  of  its 
oneness  connects  them  together.  The  identity  is  always  a 
synthesis  of  differences  which  themselves  are  not  identical 
the  one  with  the  other,  and  apart  from  these  differences  the 
identity  disappears  into  blank  indiscriminateness. 

1  will  try  to  illustrate  the  whole  question  briefly.  We  have 
a  shed  in  the  corner  of  a  field,  and  that  shed  being  burnt 
another  is  set  up  not  distinguishable  in  itself  from  the  first. 
Let  the  first  be  B  —  A  and  the  second  B  —  C  ;  in  what  sense  is  it 
true  that  what  holds  of  B  once  will  hold  of  it  always  }  The 
objection  is  obvious.  In  the  shed  B  — A  an  event  D  happened, 
but  can  we  say  that  the  event  took  place  in  B  —  C  .?  And  if 
we  can  not  say  that,  and  if  B  is  not  distinguishable,  how  are 
we  going  to  defend  our  axiom  .? 

We  are  in  no  kind  of  perplexity.  The  content  B  is 
obviously  not  the  individual  shed.  The  two  sheds  are  made 
individual  by  their  places  in  the  series,  and  those  places  fall 
outside  the  abstraction  B.  What  is  true  of  B  is  universal 
propositions  and  is  nothing  besides.  The  event  D  can  not 
be  asserted  truly  until  it  becomes  a  hypothetical  statement 
(Book  I.  Chap.  II.). 

But  the  objection  will  be  pressed,  "  The  sheds  and  their 
environment  are  a  certain  content,  and  that  content  is  the 
same.  If,  on  the  strength  of  this  content,  we  said  of  the  shed 
B  —  A  *  D  happened  here  yesterday,'  why  can  we  not  also  upon 
this  ground  now  say  of  the  shed  B  — C  'D  happened  here 
last  year.*  ?     The  content  is  what  we  go  from,  and  we  have 


Chap.  VI.]  TWO   CONDITIONS   OF  INFERENCE.  267 

that  in  both  cases."  I  reply  By  all  means :  the  content  is 
the  same.  Let  us  try  to  carry  out  the  process  you  recom- 
mend. We  can  not  of  course  connect  D  with  B  —  C  unless 
we  establish  a  chain  of  relations  through  the  identity  of  their 
end-points  {ibid.).  You  can  not  go  direct  from  the  content  B 
to  the  temporal  event  D,  for  that,  as  we  have  seen,  is  not 
predicated  categorically  {ibid.).  You  must  start  from  the 
content  as  given  in  one  time.  Well,  starting  from  B  —  A  you 
got  a  chain  of  events  which  took  you  back  to  D.  But,  if 
you  start  from  B  —  C,  you  have  a  chain  of  events  which  takes 
you  back  first  to  the  origin  of  B  —  C,  when  B  did  not  exist, 
and  then  again  through  the  destruction  of  B  —  A,  to  the  time 
when  B  once  more  existed  and  was  connected  with  D.  Your 
process  informs  you  that  D  the  event  will  not  fall  within  the 
identity  of  the  ideal  content  B  —  C.  That  content  has  been 
qualified  by  a  limitation  in  time,  and  qualified  again  by  a 
definition  of  its  component  elements,  which  excludes  their 
identity  with  the  elements  of  B  — A.  If  you  deny  that  these 
qualifications  are  objects  of  knowledge,  then  I  admit  D  is  true 
of  B  —  C,  and  why  in  the  world  should  we  7wt  think  it  true  "> 
But  if  you  admit  that  these  qualifications  are  distinctions,  then 
the  content  of  the  sheds  is  not  indiscernible,  and  therefore  by 
your  admission  is  not  identical. 

This,  I  think,  is  a  sufficient  answer  to  the  objection,  but 
it  omits  to  take  notice  of  several  difficulties.  There  are 
questions  which  no  doubt  might  occasion  us  trouble,  but  they 
do  not  seem  to  concern  us  here.  We  have  been  forced  to 
notice  a  metaphysical  problem  which,  at  least  in  this  work, 
we  can  not  deal  with,  and  hence  objections  which  we  can  not 
here  attempt  to  answer  may  be  directed  against  us.  But  at 
least  on  one  side  I  think  we  are  safe  ;  we  need  fear  no 
collision  with  the  Philosophy  of  Experience,  for  that  philo- 
sophy does  not  know  the  ground  it  stands  on.  Since  Hume's 
bold  speculations  on  the  subject  of  identity  were  suppressed 
by  himself,  the  English  school  has  repeated  a  lesson  by  rote 
and  flaunted  a  blind  ancestral  prejudice. 

§  8.  The  importance  of  the  subject  may  excuse  a  repe- 
tition. That  what  is  the  same  ideally  is  really  the  same  is 
without  any  doubt  an  enormous  assumption,  and  I  do  not  say 


268  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Ft.  L 

that  this  assumption  is  true.  What  I  do  say  is  (i)  that  all 
inference  presupposes  it,  and  (ii)  that  the  objection  to  it  rests 
on  nothing  but  metaphysics. 

(i)  If  we  only  will  look  at  the  palpable  facts,  we  must 
admit  that  logic  stands  or  falls  with  this  axiom.  Wherever 
we  join  one  premise  with  another  we  must  do  so  by  means  of 
an  identical  point,  which,  given  as  it  is  in  diverse  presenta- 
tions, is  held  to  be  the  same  because  it  has  the  same  content, 
and  which,  so  far  as  it  is  not  ideally  discernible,  is  taken  as  one. 
Failing  this  identity  the  construction  falls  apart.  I  confess  I 
do  not  know  how  to  make  this  any  clearer.  I  can  only  say 
to  any  one  who  doubts  it.  Show  me  an  inference  where  this 
does  not  hold  good,  and  I  will  show  you  a  vicious  inference, 
and  you  yourself  shall  admit  that  it  is  vicious. 

(ii)  It  sounds  terrible  to  say  that  Identity  is  an  ideal  syn- 
thesis of  differences,  and  that  this  identity  is  real  fact.  The 
words  are  strange  to  the  common  mind,  but  it  has  always 
tacitly  accepted  their  meaning.  We  believe  that  a  body  has 
changed  its  place,  but  at  the  end  of  the  movement  the  change 
that  is  past  is  no  fact  of  sense.  We  abstract  the  body  from 
its  present  position  and,  treating  this  abstraction  as  a  con- 
tinuous identity,  we  predicate  of  it  the  changing  differences. 
But  do  we  doubt  that  motion  is  a  real  fact  ?  And  if  we  are 
told.  It  is  the  material  atoms  which  are  the  same  throughout ; 
then  why  I  would  ask  do  we  take  them  for  the  same,  despite 
their  differences  of  time  and  space,  except  because  their  ideal 
content  is  the  same  ?  The  identity  of  indiscernibles  may  be 
true  or  false,  but  not  only  is  it  impossible  to  reason  without  it, 
but  it  is  the  abstract  formula  for  our  common-sense  belief. 

The  authority  of  common  sense  is  no  authority  for  me, 
but  the  result  we  have  reached  may  bring  out  one  fact.  The 
objection,  raised  by  the  Philosophy  of  Experience  against  a 
real  identity,  does  not  rest  on  any  difficulty  felt  by  common 
sense,  and  it  is  not  an  objection  it  would  ever  think  of  raising. 
It  is  a  metaphysical  objection,  and  it  rests  entirely  on  a 
metaphysical  doctrine.  It  is  because  the  Philosophy  of 
Experience  is  sure  that  there  is  no  reality  except  exclusive 
particulars,  that  it  is  horror-struck  at  the  thought  of  a  real 
universal.     And  because  its  belief  is  not  proved  nor  thought 


Chap.  VI.]  TWO  CONDITIONS  OF   INFERENCE.  269 

to  need  proof,  nor  in  any  way  discussed,  because  it  is  a  mere 
inherited  preconception  which  has  got  to  think  itself  a  real 
fact,  it  is  scarcely  so  much  to  be  called  a  doctrine  as  an 
orthodox  dogma  and  traditional  superstition. 

And,  as  it  must  happen  with  all  orthodox  dogmas,  its 
votaries  do  not  take  their  professions  in  earnest.  If  an 
universal  content  may  ever  be  real,  on  what  ground  can  they 
deny  the  identity  of  thoughts  because  one  is  yesterday  and 
the  other  to-day  ?  But  if  such  ideal  sameness  is  not  real, 
then  how  can  any  process  or  change  or  continuity  be  any- 
thing but  illusion  ?  If  a  thing  is  not  now  the  same  that  it 
waSy  if  it  is  only  alike,  then  it  can  not  have  changed.  And  if 
it  is  the  same,  on  what  ground  do  we  make  that  assertion 
except  on  the  ground  of  identity  of  content  ?  It  is  frivolous 
to  say  that  identity  may  be  real,  where  existence  is  continuous 
and  is  not  broken  in  the  series  of  time,  but  is  not  real  any- 
where else.  For  if  you  allow  that  any  lapse  or  change  is  a 
fact,  you  have  admitted  the  reality  of  an  element  not  confined 
to  this  or  that  particular,  and  you  have  admitted  it  on  the 
ground  of  the  identity  of  indiscernibles.  You  have  already 
thrown  your  principle  overboard,  and  if  it  is  false  in  one 
place  it  may  be  false  in  another.  Or  to  put  the  same  thing 
in  another  form,  if  you  are  afraid  to  break  with  common  sense 
in  one  point,  what  makes  you  so  very  bold  in  another  ?  If  I 
am  to  answer  the  question  for  you,  I  am  forced  to  say  that 
you  have  partly  no  head  and  partly  no  heart.  You  do  not 
see  the  consequences  deducible  from  your  doctrine,  and  when 
a  consequence  begins  to  look  like  a  reductio  ad  absurdum,  you 
refuse  to  follow  it.  And  this  is  what  we  call  or  used  to  call 
"  advanced  thinking." 

§  9.  It  is  against  such  opponents  that  the  syllogism  is 
right.  The  doctrine  of  copula  and  terms  which  it  cherishes 
is  indefensible,  but  it  is  right  in  demanding  an  identity  in 
reasoning.  The  middlejs  an  identity  which  connects  the  differ- 
ences, and,  being  such  an  identity,  the  middle  is  an  universal. 
In  this  point  again  the  syllogism  is  right.  For  though  the 
major  premise  is  a  superstition,  one  premise  at  least  must  be 
universal  or  else  there  can  be  no  inference  at  all.  We  have 
here  again  a  condition  necessary  to  reasoning. 


2/0  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  L 

§  ID.  We  saw  in  the  second  chapter  of  Book  I.,  and  later 
on  again  in  Chapter  VI.  §  39,  that  in  the  end  no  judgment 
is  really  particular.  They  are  all  universal.  And  we  might 
content  ourselves  here  with  recalling  the  result  we  there  have 
reached,  but  perhaps  at  the  risk  of  superfluity,  we  may  add 
some  further  remarks  on  the  subject.  If  one  of  the  premises 
were  not  universal,  how  could  they  both  have  a  common 
identity  ?  The  term  B  must  be  shared  by  both  the  premises.  It 
is  a  single  content  in  two  different  contexts.  But,  since  thus  it  is 
universal,  at  least  one  premise  must  have  the  same  character. 

This  simple  consideration  is,  I  think,  sufficient  for  any  one 
who  has  put  himself  at  the  right  point  of  view.  But  notwith- 
standing all  our  previous  discussions,  there  no  doubt  will  be 
readers  still  unwilling  or  unable  to  follow  us  in  this  argument. 
"In  'A  precedes  B  and  B  precedes  C '  can  B,"  we  shall  hear, 
"  be  really  universal  ?  Nay  even  in  the  syllogism,  if  we  take 
the  third  figure,  is  the  middle  term  really  an  universal  ?  It  is 
so  technically  because  it  is  distributed,  or  understood  in  its 
full  extension,  but  these  technical  distinctions  have  long  ago 
been  thrown  overboard,  and  with  them  has  gone  the  universality 
of  singulars."     I  will  briefly  reply  to  the  above  objection. 

§  II.  An  universal  judgment  is  one  that  holds  of  any 
subject  which  is  a  synthesis  of  differences.  It  is  a  proposition 
the  truth  of  which  is  not  confined  to  any  single  this.  The 
subject  extends  beyond  the  judgment,  and,  where  the  subject 
goes,  the  judgment  is  true.  In  this  sense  we  have  seen  that 
all  judgments  are  universal.  But  we  are  limited  here  to  a 
simpler  issue,  for  we  have  to  show,  given  a  valid  inference, 
that  at  least  one  premise  is  universal.  It  is  quite  enough,  as  we 
have  just  remarked,  to  consider  the  identity  of  the  middle  term  : 
but  a  more  detailed  exposition  may  perhaps  be  welcome. 

There  are  certain  cases  which  call  for  no  discussion. 
Where  the  middle  term  is  an  abstract  attribute,  and  this 
forms  the  subject  of  one  of  the  premises,  there  one  premise 
must  be  allowed  to  be  universal.* 

*  In  order  to  bring  arguments  into  this  form  we  may  freely  convert 
any  negative  judgments.  Thus  in  the  second  figure  we  may  convert,  as 
required,  negative  premises  or  conclusions.  The  case  of  Baroco  presents 
no  difficulty. 


Chap.  VI.J  TWO  CONDITIONS   OF  INFERENCE.  IJl 

The  difficulty  which  is  felt  arises  from  those  cases  where 
the  middle  term  is  a  singular,  or  where  it  is  not  the  ostensible 
subject  of  either  premise.  Take  for  instance  "  A  is  to  right  of 
B,  and  B  of  C,  and  therefore  A  of  C,"  or  "  A  and  C  have 
the  note  B  in  common,  and  therefore  C  is  in  tune  with 
A,  and  both  related  by  the  identity  of  B."  How  in  such 
inferences  as  these  can  we  show  that  one  premise  must  be 
universal } 

§  12.  Unless  our  previous  discussions  have  led  us  quite 
wrong,  such  a  question  as  this  can  be  readily  answered. 
"  B  is  to  right  of  C  "  is  an  universal  judgment  because  B  is  an 
identity  which  has  the  differences  of  its  spatial  relations  to  A 
and  C.  It  transcends  the  context  B-C  and  is  therefore 
universal.  Or,  from  another  point  of  view,  the  relation  B  —  C 
is  true  of  a  subject  which  extends  itself  beyond  those  limits, 
and  is  the  identical  subject  of  which  the  relation  A  —  B  is  also 
true.  If  you  take  the  relations  as  qualifying  B,  then  B  is  the 
universal  which  exhibits  these  differences.  Or  again  if  you 
go  somewhat  further  back,  then  the  unity  of  the  common 
space  is  the  genuine  subject  of  which  these  relations  are  diverse 
attributes.  We  can  always  find  an  identical  subject  although 
that  subject  need  not  be  apparent.  In  "  Caesar  is  angry  and 
Caesar  is  silent,  and  therefore  silence  may  accompany  anger," 
it  is  the  grammatical  subject  which  supplies  the  universal 
within  whose  identity  the  synthesis  holds  good.  But  where 
from  "  A  has  a  certain  note  B  and  C  has  also  the  self-same 
note,"  we  infer  a  relation  between  A  and  C,  it  is  doubtful 
where  the  actual  subject  lies.  If  we  are  willing  to  accept  the 
grammatical  subject,  then  in  "  C  has  the  note  B,"  C  is  our 
universal.  For  C  is  disturbed  from  its  original  context  and 
expanded  ideally  so  as  to  form  a  whole  with  A.  And,  if  it 
were  not  universal,  it  could  not  be  treated  as  a  subject  waiting 
to  receive  a  predicate  beyond  its  original  given  existence.* 
This  would  be  the  right  interpretation  if  A  and  C  are  to  be 
considered  as  subjects.  But  it  is  better  here,  I  think,  to  take 
the  middle  as  the  actual  subject  of  both  the  premises.  B  is 
the  universal  of  which  we  predicate  the  difference  B  —  A  and 

*  Of  course  if  you  suppose  the  relation  A  —  C  to  be  a  perception  got 
simply  from  the  given,  then  there  is  no  inference  and  cadit  qucEstio. 


2/2  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  L 

the  difference  B  — C,  and  it  is  the  bond  of  identity  which 
interrelates  the  whole. 

§  13.  We  shall  see  hereafter  that  every  inference  may  be 
taken  as  holding  within  the  identity  of  one  subject  (Book  III. 
Part  I.  Chap.  VI.  §  34),  and  if  we  take  this  view  it  is  obvious 
that  the  subject  of  both  premises  is  universal.  For  the 
present  it  may  prove  sufficient  to  remember  that,  inference 
being  an  ideal  construction  and  involving  therefore  an  ideal 
centre,  one  premise  must  be  taken  as  true  beyond  the  limits 
of  a  particular  subject.  If  we  keep  hold  of  this  reflection  we 
shall  not  be  shaken  by  any  puzzles  which  are  laid  before  us. 
In  the  previous  Book  I  have  endeavoured  to  anticipate  and 
to  cut  the  root  of  those  difficulties  which  are  the  most  likely 
to  be  raised,  and  it  is  to  the  discussions  of  that  Book  that  I 
must  refer  back  the  reader  who  is  still  inclined  to  hesitate. 

In  the  ensuing  Part  of  the  present  Book  we  shall  criticize 
some  inadequate  views  of  inference,  and  shall  begin  with  that 
belief  v/hich  is  most  opposed  to  the  doctrines  set  forth  in  the 
present  Chapter. 


(     273     ) 


BOOK   II.— PART  II. 


CHAPTER  I. 

THE   THEORY   OF  ASSOCIATION   OF   IDEAS. 

§  I.  The  end  we  had  before  us  in  the  first  part  of  this  Book 
was  to  give  a  general  account  of  inference.  The  account  was 
in  a  certain  sense  provisional,  since  the  examples  it  dealt  with 
did  not  pretend  to  illustrate  every  kind  of  inference.  But 
within  those  limits  the  result  we  arrived  at  seemed  irrefragably 
true.  The  end  we  have  before  us  in  this  Second  Part,  is  the 
criticism  and  refutation  of  certain  theories  which  are  out  of 
harmony  with  the  conclusion  we  have  reached. 

The  title  of  this  chapter  calls  for  explanation.  "The 
Association  of  Ideas,"  it  may  be  objected,  "  is  not  so  much  a 
theory  as  a  fact ;  a  fact  which  on  the  one  hand  is  quite 
indisputable,  and  which  on  the  other  hand  can  be  discrepant 
with  no  theory  except  a  theory  which  runs  counter  to  fact." 
But  the  objection  would  rest  on  an  entire  misunderstanding. 
The  psychological  fact  of  "Association"  is  of  course  un- 
questionable. The  account  of  that  fact  which  is  given  by  the 
orthodox  English  philosophy,  is  in  my  judgment  not  only 
questionable  but  false.  And,  beside  being  false,  it  is  incom- 
patible with  any  tolerably  accurate  theory  of  reasoning.  For 
the  universality  and  identity,  which  we  saw  were  necessary  for 
every  inference,  do  not  exist  in  the  theory  of  "  Experience." 
We  are  offered  in  their  stead  a  fictitious  substitute,  which  does 
not  exist  and  therefore  can  not  work,  and  which  would  not 
work  even  if  it  existed. 

§  2.  "  Inseparable   Association,"   and   the    "  Chemistry   of 

T 


2/4  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  IL 

Ideas,"  are  phrases  which  are  only  too  familiar  to  most  of  us. 
They  recall  a  controversy  which  has  served  in  some  measure 
to  obscure  the  questions  it  professed  to  elucidate.  But  the 
more  refined  developements  of  the  Association  doctrine  do 
not  immediately  concern  us  here.*  For  they  have  no  direct 
bearing  on  the  theory  of  inference  ;  and  it  is  solely  as  it 
touches  the  subject  of  reasoning  that  we  have  here  to  do  with 
Association.  We  may  confine  our  attention  to  the  common 
doctrine,  as  exemplified  in  the  ordinary  working  of  the  Laws 
of  Resemblance  and  Contiguity. 

§  3.  The  "  association  of  ideas  "  is  a  phrase  which  may  be 
taken  to  express  a  well-known  psychological  fact.  And  if 
taken  so,  it  is  nothing  but  a  title.  The  fact,  which  it  stands 
for,  is  a  familiar  experience,  and  the  meaning  of  the  title  is 
not  proposed  as  an  accurate  theory  of  that  fact.  It  is  a  name 
which  must  not  be  pressed  into  a  doctrine. 

But,  as  understood  by  the  Philosophy  of  Experience,  the 
"  association  of  ideas  "  has  long  ceased  to  be  a  way  of  marking 
a  thing  which  we  all  admit  has  real  existence.  It  has  become 
the  battle-cry  of  a  school,  and  a  metaphysical  doctrine  and 
theory  of  things.  It  contains  a  belief  as  to  the  nature  of  the 
mind,  or  at  least  as  to  the  mode  in  which  the  mind  works, 
which  is  irreconcileable  with  the  views  we  have  already 
adopted.  Hence  if  "  association "  is  to  stand  for  a  mere 
psychological  fact,  then  of  course,  like  every  one  else,  I  believe 
in  it  ;  and  I  propose  to  give  here  the  explanation  of  that  fact. 
But,  if  "  association  "  means  that  view  of  the  fact  which  has 
been  embraced  by  a  certain  school,  then  I  do  not  believe  in  it ; 
and  I  propose  to  show  that  in  this  latter  sense  "  association  " 
has  no  real  existence.  It  has  not  only  been  extended  to  take 
in  phenomena  which  can  not  properly  come  within  its  limits, 
but  within  any  limits,  however  narrow,  it  is  a  false  view  of 
things. 

§  4.  The  word  Association,  I  suppose,  implies  properly 
some  kind  of  voluntary  union.  That  signification  of  course 
disappears,  but  it  leaves  a  shade  of  meaning  behind.  For 
things  are  not  associated  by  their  own  necessity,  and  by  virtue 
of  some  internal  connection.  Such  a  group  as  the  farnily,  and 
*  We  shall  append  some  remarks  at  the  end  of  this  chapter. 


Chap.  I.J      THE   THEORY   OF   ASSOCIATION   OP^   IDEAS.  2/5 

even  the  state,  can  hardly  be  called  associations  in  any  strict 
sense.  Association  implies  chance,  that  is,  it  depends  on 
circumstances  external  to  that  which  is  conjoined.  And  so, 
when  we  use  the  term,  we  must  be  taken  to  suggest  that,  if 
A  and  B  had  not  been  associated,  they  would  nevertheless 
have  been  A  and  B.  For  the  conditions,  which  happened  to 
bring  them  together,  do  not  follow  in  fact,  nor  are  deducible 
in  idea,  from  the  existence  or  character  of  mere  A  and  B.  We 
may  perhaps  explain  by  a  reference  to  the  hypothetical 
judgment.  In  such  a  judgment,  if  the  condition  is  known, 
you  assert  not  a  conjunction  but  always  a  connection.  But 
in  a  categorical  judgment  of  perception,  and  that  means  in  a 
hypothetical  judgment  where  the  condition  is  unknown,  you 
assert  a  conjunction  and  not  a  connection.  The  former  word 
corresponds  to  Association.  The  conjunction  with  B  is  pre- 
dicated of  A  on  the  strength  of  a  condition,  that  does  not 
come  into  the  subject,  but  is  imported  by  the  force  of  such 
circumstances  as  in  their  relation  to  A  are  chance. 

Association  thus  comes  to  mean  chance-conjunction,  and 
in  our  mental  history  we  find  of  course  very  often  that  ideas 
are  conjoined  by  the  merest  accident.  If  you  take  these 
ideas  and  consider  them  by  themselves,  you  can  find  no  con- 
nection and  no  reason  for  their  union.  Mere  circumstances, 
which,  so  far  as  the  ideas  are  concerned,  might  never  have 
existed,  did  bring  them  together.  And  a  union  caused  by 
such  chance-conjunction  is  the  common  meaning  of  Mental 
Association.  In  this  sense  of  the  term  it  answers  to  that 
which,  I  suppose,  we  all  admit  to  be  fact ;  but  it  conveys  no 
theory  of  any  kind  whatever.  It  makes  no  assertion  as  to  the 
nature  of  ideas,  and  it  makes  no  assertion  as  to  the  laws  of  their 
reproduction.  It  calls  attention  to  one  fact  among  others.  It 
does  not  profess  to  reduce  well-nigh  everything  in  the  mind 
but  sensations,  impressions,  or  feelings,  to  this  single  fact. 

§  5.  The  school  of  Experience,  in  its  more  consistent 
developement,  has  turned  the  metaphorical  expression  of  one 
fact  into  a  theory  which  may  be  said  to  cover  all.  It  has  a 
doctrine  as  to  the  ultimate  constituents  of  mind.  They  are 
particular  feelings  and  particular  ideas,  in  either  case  repellent 
units.     And  they  have  absolutely  no  internal  bond  of  con- 

T  2 


2/6  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Ft.  IL 

nection.  There  is  no  ground  common  to  the  different  units, 
which  could  serve  as  a  real  basis  for  their  union.  Univer- 
sality and  identity  are  derided  as  fictions.  In  the  procession 
of  these  units  we  may  separate  two  trains,  the  train  of 
sensations  and  the  train  of  ideas  ;  but  these  all  are  separate 
individual  realities.  "  All  our  distinct  perceptions  are  distinct 
existences,  and  the  mind  never  perceives  any  real  connection 
among  distinct  existences "  (Hume).  The  philosophy  of 
Experience  is  psychological  Atomism. 

There  is  nothing  which  the  atoms  possess  in  common,  and 
there  could  be  no  "  real  connection  "  between  them.  They 
are  conjoined  by  the  agency  of  chance  or  fate.  That  im- 
pressions should  come  to  us  in  a  certain  arrangement,  and 
should  in  some  cases  precede  feebler  counterparts  of  them- 
selves— this  springs  from  the  unknown  necessity  of  a  nature, 
which  we  can  not  say  is  the  nature  of  the  units.  And  the 
secondary  conjunction  of  impressions  with  ideas  and  of  ideas 
with  one  another,  what  is  this  but  the  accident  of  Association, 
whose  laws  are  nothing  but  general  expressions  for  certain 
recurring  kinds  of  irrational  combination  ?  Destiny  and 
chance  are  two  names  of  one  lord  that  sways  the  procession 
of  fleeting  units.  In  their  short-lived  occupation  of  that  void 
which  is  the  soul,  they  are  combined  by  the  accident  of 
presentation  or  by  the  fate  of  association.  And  the  "  final 
inexplicability  "  of  J.  S.  Mill  may  recall  an  echo  of  the  "  free 
will "  of  Epikurus. 

§  6.  Having  thus  anticipated  by  a  sweeping  theory  the 
nature  of  everything  that  is  to  be  experienced,  the  school  for 
the  future,  so  long  as  it  keeps  true  to  the  metaphysical 
doctrine  on  which  it  stands,  may  call  itself  the  Philosophy  of 
Experience.  And  it  is  also  analytical ;  for  does  it  not  assume 
that  every  complex  phenomenon  of  the  mind  is  resolvable 
into  the  units  which  its  theory  has  established .?  Its  first 
principles  no  doubt  are  never  analyzed ;  but  analysis,  it  is 
obvious,  must  be  broken  off  somewhere.  If  the  "  analytical 
school "  are  content  to  stop,  then  the  limit  of  human  thinking 
has  been  reached.  If  the  Philosophy  of  Experience  is  content 
with  the  result,  then  surely  the  product  of  analysis  must  be 
fact.     Analysis  in   the  future  will  consist  In  the  attempt  to 


Chap.  I.]      THE   THEORY   OF   ASSOCIATION   OF   IDEAS.  277 

reconstruct  synthetically  the  phenomena  of  the  mind  from 
elements  gained  in  accordance  with  first  principles,  and 
according  to  the  Laws  which  first  principles  have  established 
(cf  Book  III.  Part  I.  Chap.  VI.  §  10).  It  is  hardly  necessary 
that  in  every  case  the  existence  of  each  element  should  be 
verified  a  posteriori.  If,  for  the  explanation  of  visual  exten- 
sion, it  were  first  necessary  to  verify  in  actual  observation  the 
fact  of  colour-sensations  devoid  of  all  extension,  it  is  possible 
that  the  analysis  could  not  be  performed.  And,  since  that 
analysis  has  been  firmly  established,  it  is  clear  that  its  basis 
can  not  be  unreal.  If  we  confine  ourselves  to  the  limits  and 
the  method  of  the  school  of  Experience,  we  may  be  sure  of 
one  thing ;  if  we  are  true  to  Experience  we  must  be  true  to 
fact. 

§  7.  We  can  appreciate  now  the  nature  of  the  claim  which 
is  laid  to  the  titles  of  "  experience  "  and  "  analysis."  But  we 
must  hasten  to  examine  the  character  of  those  Laws  which 
rule  the  void  and  which  move  ideas.  They  answer,  in  the 
psychical  empty  space,  to  what  is,  called  "  cohesion "  or 
"attraction"  in  the  external  void  (Hume,  Treatise  I.  i.  4). 
The  two  main  principles  are  the  law  of  Contiguity,  and  the 
law  of  Similarity  or  Agreement. 

I.  "  Actions,  Sensations,  and  States  of  Feeling,  occurring 
together  or  in  close  succession,  tend  to  grow  together,  or 
cohere,  in  such  a  way  that,  when  any  one  of  them  is  after- 
wards presented  to  the  mind,  the  others  are  apt  to  be  brought 
up  in  idea."     Bain,  Senses,  p.  327. 

II.  ''''Present  Actions,  Sensations,  Thoughts,  or  Emotions 
tend  to  revive  their  LIKE  among  previous  Impressions,  or 
States."     Ibid.  p.  457. 

Or,  to  put  the  same  thing  in  the  opposite  order,  "  Of  these 
laws  the  first  is,  that  similar  ideas  tend  to  excite  one  another. 
The  second  is,  that  when  two  impressions  have  been  frequently 
experienced  (or  even  thought  of)  either  simultaneously  or  in 
immediate  succession,  then  whenever  one  of  these  impressions, 
or  the  idea  of  it,  recurs,  it  tends  to  excite  the  idea  of  the 
other."     J.  S.  Mill,  Logic,  II.  p.  440,  Ed.  IX. 

A  briefer,  and  on  the  whole  more  accurate  expression,  would 
perhaps  be  this  ;  Mental  units  which  have  co-existed  cohere, 


2/8  THE   PRINCIPLES   OF  LOGIC.  [Bk.  II.  Pt.  II. 

and  mental  units  which  are  like  recall  one  another — at  least  in 
image. 

§  8.  In  saying  that  I  entirely  and  utterly  reject  each  one 
of  these  statements,  I  may  be  taken  to  deny  the  existence  of 
fact.  But  (to  repeat  once  more  a  distinction  I  have  drawn) 
what  I  find  it  impossible  to  make  myself  believe  is  not  the 
fact  which  these  formulae  may  be  taken  as  loosely  indicating. 
It  is  on  the  contrary  their  theory  of  that  fact  which  I  can  not 
swallow.  And  I  have  no  insurmountable  objection  to  the  use 
of  such  statements  ;  but  I  can  not  for  one  moment  allow  that 
they  are  true. 

I  shall  give  hereafter  in  greater  detail  those  reasons  which 
lead  me  to  believe  that  these  laws  are  nothing  but  fictions. 
But  the  main  ground  of  objection  may  be  stated  at  once. 
The  ideas  which  are  recalled  according  to  these  laws  are 
particular  existences.  Individual  atoms  are  the  units  of 
association.  And  I  should  maintain,  on  the  contrary,  that 
in  all  reproduction  what  operates  everywhere  is  a  common 
identity.  No  particular  ideas  are  ever  associated  or  ever 
could  be.  What  is  associated  is  and  must  be  always 
universal. 

It  will  be  found,  I  think,  the  most  convenient  course,  if 
I  first  give  some  account  of  the  way  in  which  I  conceive 
association  is  effected,  and  then  attempt  to  show  that  the 
method,  commonly  accepted  as  fact,  is  wholly  fictitious. 

§  9.  In  the  previous  Book  (p.  36,  foil.)  I  have  to  some  ex- 
tent anticipated  this  discussion,  and,  trusting  that  the  result 
to  which  we  there  came  may  be  recalled  by  the  reader,  I  may 
perhaps  be  here  allowed  to  be  brief.  I  have  no  hope  of 
persuading  the  orthodox  believer,  and  others  may  be  willing 
to  help  in  working  out  the  sketch  of  a  doctrine. 

The  main  Law  of  Reproduction  may  be  laid  down  thus  ; 
Any  part  of  a  single  state  of  mind  tends,  if  reproduced,  to 
re-instate  the  remainder  ;  or  Any  element  tends  to  reproduce 
those  elements  with  which  it  has  formed  one  state  of  mind. 
This  may  be  called  the  law  of  Redintegration.  For  we  may 
take  this  name  from  Sir  W.  Hamilton  {Reid,  p.  897),  having 
found  nothing  else  that  we  could  well  take. 

There  are  several  points  in  the  formula  which   call    for 


Chap  L]      THE   THEORY   OF  ASSOCIATION   OF   IDEAS.  279 

explanation.  We  might  ask,  in  the  first  place,  What  is  a 
sinsfle    state    of  mind  ?      Does    it  exclude    succession  ?      It 

o 

certainly  does  not  do  so.  It  may  be  further  defined  as  any 
psychical  complex  which  is  present  together,  presence  signify- 
ing presentation,  a  certain  direct  relation  to  the  mind  which 
does  not  imply  succession  in  time.  As  I  have  endeavoured 
(p.  52)*  to  throw  some  light  on  the  meaning  of  this  term,  I 
must  iJe  excused  from  a  further  discussion  of  it  here. 

In  the  second  place  the  "  parts  "  of  this  present  state  need 
not  be  either  perceptions  or  ideas.  For  the  formula  includes 
every  possible  kind  of  mental  element ;  and  this  is  the  reason 
why  we  can  not  accept  the  principle  as  we  find  it  laid  down 
by  Wolff  and  others.  I  will  not  here  ask,  if  in  the  end  it 
is  not  possible  that  association  is  confined  to  intellectual 
or  perceptive  elements  (vid.  Book  III.  I.  Chap.  III.  §§  20- 
22).  It  is  better  for  ordinary  purposes  to  suppose  that  it 
also  applies  to  desires  and  feelings.  But  subject  to  this 
correction  we  may  adopt,  if  we  please,  Wolff's  statement  of 
the  law. 

"  Si  quae  simul  percepimus  et  unius  perceptio  denuo  pro- 
ducatur,  sive  sensuum  sive  imaginationis  vi ;  imaginatio 
producit  et  perceptionem  alterius — seu  quod  perinde  est — 
perceptio  praeterita  integra  recurrit,  cujus  praesens  continet 
partem  "  {Psych.  Emp.  §  104). 

Maas,  following  Wolff,  has  thus  formulated  the  principle. 
"Given  an  idea  or  perception,  then  all  those  ideas,  which 
belong  with  it  to  one  total  perceptive  state,  may  immediately 
associate  themselves  with  it,  and  no  other  ideas  can  do  so." 
Or  "  Every  idea,  or  perception,  recalls  to  the  mind  its  total 
perceptive  context"  (Versiich,  Verb.  Ausg.  1797,  §  13). 

This  law  of  Redintegration,  we  must  bear  in  mind,  does 
not  exclude  any  succession  of  events  which  comes  as  a  whole 
before  the  mind ;  and  it  is  not  to  be  confined  to  perceptions 
and  ideas. 

§  10.  The  law  of  redintegration  is  a  very  different  thing 
from  the  law  of  contiguity,  as  that  is  understood  by  the 
school  of  Experience.  Superficially  alike,  they  are  separated 
by  the  chasm  that  divides  irreconcileable  views  of  the  world. 
For  contiguity  is  cohesion  between  psychical  units,  and  its 


280  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  II. 

elements  are  particular  existing  phenomena.  What  it  couples 
is  the  actual  individual  impression  or  image,  as  such.  It  is 
not  association  between  universals.  But  Redintegration  is  not 
anything  else.  For  it  never  re-instates  the  particular  fact.  It 
can  not  deal  with  anything  that  could  be  a  phenomenon,  or 
could  ever  exist.  It  does  not  couple  psychical  units,  but  is 
entirely  confine^  to  what  is  universal. 

We  should  find  it  hard  to  overstate  the  enormous  diver- 
gence of  these  two  interpretations  of  the  fact  of  association. 
Contiguity  asserts  a  conjunction  between  existences.  Red- 
integration asserts  a  connection  between  universals,  which  as 
such  do  not  exist.  What  operates  in  the  first  is  an  external 
relation  between  individuals.  What  works  in  the  second  is  an 
ideal  identity  within  the  individuals.  The  first  deals  with 
the  that,  and  the  second  with  the  what.  The  first  unites  facts, 
and  tl}j^  second  mere  content. 

According  to  the  view  which  to  me  seems  the  truth,  to 
talk  of  an  association  between  psychical  particulars  is  to  utter 
mere  nonsense.  These  particulars  in  the  first  place  have  got 
no  permanence ;  their  life  endures  for  a  fleeting  moment. 
In  the  second  place  they  can  never  have  more  than  one 
life  ;  when  they  are  dead  they  are  done  with.  There  is  no 
Hades  where  they  wait  in  disconsolate  exile,  till  Association 
announces  resurrection  and  recall.  When  the  fact  is  bodily 
buried  in  the  past,  no  miracle  opens  the  mouth  of  the  grave 
and  calls  up  to  the  light  a  perished  reality,  unchanged  by  the 
processes  that  rule  in  nature.  These  ^  touching  beliefs  of  a 
pious  legend  may  babble  in  the  tradition  of  a  senile  psy- 
chology, or  contort  themselves  in  the  metaphysics  of  some 
frantic  dogma,  but  philosophy  must  register  them  and  sigh 
and  pass  on. 

There  is  nothing  we  know  which  can  warrant  the  belief 
that  a  particular  fact  can  survive  its  moment,  or  that,  when  it 
is. past,  it  can  ever  live  again.  We  know  it  is  true  in  our 
actual  experience  that  reproduction  presents  us  with  particular 
images  ;  but  to  assert  that  these  are  the  perished  originals  is 
to  demand  a  miracle  to  support  our  false  beliefs.  We  have 
absolutely  no  kind  of  warrant  in  experience  for  our  assurance, 
that  what  comes  into  the  mind  by  Association  is  the  particular 


CuAP.  I.]      THE   THEORY   OF   ASSOCIATION   OF   IDEAS.  28 1 

as  we  had  it.  For  the  particular  fact  is  made  particular  by 
an  elaborate  context  and  a  detailed  content.  And  this  is  not 
the  context  or  content  which  comes  back.  What  is  recalled 
has  not  only  got  different  relations  ;  itself  is  different.  It 
has  lost  some  features,  and  some  clothing  of  its  qualities,  and 
it  has  acquired  some  new  ones.  If  then  there  is  a  resurrection 
assuredly  what  rises  must  be  the  ghost  and  not  the  individual. 
And  if  the  ghost  is  not  content  with  its  spiritual  body,  it  must 
come  with  some  membersVhich  are  not  its  own.  In  the  hurry 
of  the  moment,  we  have  reason  to  suspect,  that  the  bodies  of 
the  dead  may  be  used  as  common  stock. 

But  if  we  are  willing  to  throw  over  our  orthodox  creed,  we 
may  escape  with  less  demand  on  our  faith.     The  doctrine 
of  Redintegration  does  not  ask  us  to  subscribe  to  the  belief 
that   what   is   past   exists    over  again.       It  offers    a  simpler 
explanation  of  the  facts.     Given   any  presentation    X,  which 
has  a  content  such  as  .  .  .  a  b  c  d  e  .  .  .  ,  it  asserts  that  the  one- 
ness of  this  presentation  is  in  a  certain  sense  a  connection  of 
its   content.     The   fact  of  the   presentation   absolutely   dis- 
appears.     What  is   left  behind  is  a  mental  result,  into   the 
ultimate   metaphysical  nature  of  which  we  do  not  here  en- 
quire.    But  this  result  is  not  a  phenomenon,  not  a  particular 
image  or  relation  of  such  images.     It  is  an  alteration  of  the 
mind,  which  shows  itself  to  us  as  a  tendency  to  pass  from 
content  to  content.     It  is  a   connection,  not  between  this  a 
and  this  b,  or  this  c  and  this  d,  but  between  the  universals 
a   and  b,  or  c  and  d.      It  is  a  quality  of  the    mind   which 
manifests  itself  in  the  fact  that,  if  we  have  one  part  of  the 
content  which  appeared  in  X,  then — although  everything  which 
particularized  that  content  in  X,  and  gave  it  existence,  has 
disappeared — this  bare  universal  a,  b,  c,  or  d,  when  given  with 
a   different   set  of   particulars,    may   re-instate   by   its   ideal 
identity  any  other  of  the  universals,  a,  b,  c,  or  d.     It  will  recall 
it  certainly  in  a  particular  clothing,  but  this  clothing  will  be 
determined  by  present  mental  circumstances,  and  will  not  be 
the  clothing  of  its  past  existence.     And  this  particular  clothing, 
again  and  in  the  second  place,  is  not  the  bond  which  works  in 
the   reproduction.      What  works  is  the  connection  between 
the  universals,    and  the  basis  of  that   working    is  the  ideal 


282  THE   PRINCIPLES   OF   LOGIC.  [Bk.  H.  Pt.  XL 

identity  of  some  element  in  what  is  present  and  in  what  is 
past. 

§  II.  I  have  illustrated  my  meaning  already  by  anticipa- 
tion (p.  37),  and  shall  illustrate  it  hereafter.  At  present  I 
must  hasten  to  meet  an  objection.  I  maintain  that  all 
association  is  between  universals,  and  that  no  other  association 
exists.  Every  kind  of  reproduction,  in  my  judgment,  takes 
place  by  virtue  of  identity  plus  the  connection  of  universals. 
"  And  do  you  really,"  there  may  here  come  a  protest,  "  do 
you  really  believe  this  holds  good  with  emotions  ?  If  castor- 
oil  has  made  me  sick  once,  so  that  I  can  not  see  it  or  even 
think  of  it  v/ithout  uneasiness,  is  this  too  a  connection  between 
universals  1 "  I  reply  without  hesitation  that  I  believe  it  is 
so ;  and  that  I  must  believe  this  or  else  accept  a  miracle,  a 
miracle  moreover  which  is  not  in  harmony  with  the  facts  it 
is,  invoked  to  explain.  You  believe  then,  I  feel  inclined  to 
reply,  that  the  actual  feelings,  which  accompanied  your  vomit- 
ing, have  risen  from  the  dead  in  a  paler  form  once  more  to 
trouble  you.  I  could  not  credit  that  even  if  it  answered  to 
the  facts.  And  it  does  not  answer,  since  the  new  feeling  is 
clearly  different  from  the  old  one.  The  old  feeling  was  the 
event  it  was,  by  its  presence  in  a  certain  series  of  events.  It 
had  a  number  of  accompaniments,  conditions,  and  circum- 
stances, which  belonged  to  it  as  this  feeling.  The  psycholo- 
gical environment  was  in  great  part  different.  Nay,  if  we 
could  observe  it,  we  should  probably  find  that  its  actual 
internal  content  has  varied.  We  should  see  degrees  or  shades 
of  quality,  which  in  the  two  cases  would  probably  not  be 
the  same.  Your  miraculous  supposition  is  therefore  not  even 
a  fiction  which  will  work. 

And  if  you  say  that,  by  the  sameness  of  the  feeling,  you 
mean  a  feeling  which  is  the  same  in  kind,  and  for  all  practical 
purposes  one  with  the  other,  this  is  exactly  the  thesis  which 
I  wish  to  establish,  and  which  you  have  objected  to.  The 
feelings  of  sickness  are  the  same  in  the  main,  that  is,  they 
have  an  identical  content,  which  is  the  same  although  the 
contexts  are  different.  But,  if  so,  is  it  not,  I  would  ask, 
admitted  that  what  is  reproduced  is  not  the  particular  but  is 
the  universal  ?     The  first  conjunction  of  castor-oil  and  sickness 


Chap.  L]      THE   THEORY   OF   ASSOCIATION   OF   IDEAS.  283 

has  no  longer  the  smallest  existence  as  fact.  But  it  gave  rise 
to  a  connection  of  elements  in  the  mind,  which  elements  are 
an  idealized  part  of  the  content  of  this  perished  fact.  The  new 
presentation  of  castor-oil  is  a  fact  which  is  certainly  not  the  old 
fact ;  yet  it  has  a  content  which  is  partly  the  same.  The  pre- 
sence of  this  identical  universal  supplies  the  antecedent  to  the 
hypothetical  connection  of  elements  in  the  mind,  and  this  then 
passes  from  hypothesis  into  actual  fact.  In  other  words  the  ideal 
identity  of  this  castor-oil  with  that  castor-oil  recovers  ideally, 
and  in  an  universal  form,  another  element  of  the  original 
context.  And,  so  far  as  mere  reproduction  goes,  nothing  but 
the  universal  could  ever  be  called  up.  It  is  the  fresh  pre- 
sentatiojt  which  adds  detail  to  the  reproduced  element.  This 
new  perception  re-particularizes  the  universal,  and  does  so  in 
a  way  which  will  not  be  the  old  way,  and  in  many  cases  will 
be  strikingly  different.  But  such  re-particularization  (if  the 
term  may  be  allowed)  is  not  association,  and  is  not^  repro- 
duction. For  though  the  new  particular  feeling  of  sickness  is 
no  doubt  the  r^i-?/// of  reproduction,  yet /^  never  was  associated, 
and  it  can  not  have  been  reproduced,  since  it  exists  now  for 
the  first  time.  You  may  say  that  by  a  miracle  the  old  feeling 
of  sickness  without  detriment  to  its  sameness  has  been  changed 
en  route ;  but  this  very  change  and  this  very  difference  is  the 
denial  of  your  doctrine,  unless  your  doctrine  too  is  from  time 
to  time  changed  by  a  parallel  miracle. 

I  do  not  say  that  we  should  be  right  to  reduce  all  repro- 
duction to  logical  redintegration.  That  is  a  point  on  which  I 
shall  touch  hereafter  (Book  III.  I.  Chap.  III.  §  20).  It  does  not 
concern  us  here.  For  it  is  not  necessary  to  believe  that  the 
"  idea "  of  a  feeling  is  a  logical  idea,  and  that  it  is  a  con- 
scious or  even  an  unconscious  symbol.  What  must  however 
be  believed  is  that  it  is  an  universal.  And  this  need  give 
rise  to  not  the  smallest  psychological  difficulty.  Whatever 
differences  may  separate  the  various  kinds  of  psychical 
phenomena,  they  are  all  alike  in  one  point.  They  all  have 
content  as  well  as  existence.  They  are  not  confined  to  the 
"that,"  but  each  has  a  "what,"  since  there  is  a  complex 
quality  and  relations  of  quality.*  And,  this  being  so,  we 
*  Quality  at  this  stage  covers  quantity. 


284  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  XL 

have  all  that  is  required  for  the  formation  of  universals.  For 
an  identity  of  content  in  different  contexts  is  and  must  be  an 
universal,  whether  we  are  dealing  with  perceptions  or  feeljjags 
or  volitions.  / 

§  12.  To  suppose  the  presence  and  the  operation  of 
universals  in  all  reproduction,  introduces  a  unity  into  our 
view  of  the  soul.  It  enables  us  to  interpret  all  stages  of 
mind  as  the  growth  of  one  principle.  We  can  thus  accept 
without  abridgment  the  very  highest  phenomena,  and  we  can 
show  their  root  in  the  lowest  and  rudest  beginnings  of  the 
soul.  We  may  say  that  experience  will  begin  when  a  present 
perception  has  one  part  of  its  content  identical  with  a  past, 
and  when  this  common  universal  re-instates  another  part  of  the 
original  context.  But  that  past  element  most  certainly  does 
not  reappear  in  its  particular  form.  It  too  is  universal,  and 
it  is  the  connection  of  these  universals  which  operates  in  the 
mind.  Hence  the  content  of  the  perception,  which  is  now 
present,  is  extended  by  means  of  this  ideal  synthesis,  and, 
itself  individual,  individualizes  the  result.  This  true  account 
is  in  harmony  with  fact.  But,  on  the  other  hand,  to  suppose 
that  one  or  more  particular  feelings  or  images  are  magically 
recalled  and  adhere  to  the  perception,  is  directly  contrary  to 
the  plain  facts  of  observation.  For  these  separate  particulars 
are  palpably  absent ;  and  in  order  to  explain  their  obvious 
absence  it  is  necessary  to  invoke  a  Law  of  Obliviscence,  by 
which  their  details  may  again  be  shorn  off.  But  this  Law  of 
Obliviscence  has  no  title  to  exist  in  the  shape  which  is  given 
to  it,  except  that  it  is  demanded  by  an  erroneous  theory 
(vid.  inf  §  25).  A  miracle  is  first  invoked  to  explain  the 
facts,  and  then  a  fiction  introduced  to  square  the  facts  to  the 
miracle. 

But  the  unviolated  facts  support  redintegration  by  identity. 
In  a  rudimentary  soul  a  present  sensation  has  its  content 
increased  by  internal  extension.  There  are  not  several  facts 
before  the  mind,  but  there  is  a  single  fact  whose  content, 
after  enlargement,  consists  in  part  of  an  unconscious  inference. 
The  sensation  is  extended  by  an  ideal  supplement,  and  this 
supplement,  through  union  with  the  individual  sensation, 
becomes  for  the  mind  individual  fact.     On  this  view  there  is 


Chap.  I.]      THE    THEORY   OF   ASSOCIATION    OF   IDEAS.  285 

no  psychical  phenomenon  which  intervenes  between  the 
sensation  and  the  resulting  perception.  We  have  not  to 
postulate  the  irrelevant  and  conflicting  detail  of  particular 
images,  and  have  no  need  to  rid  ourselves  of  this  palpable 
fiction  by  any  arbitrary  Law.  Or  again,  if  the  result  of  the 
new  sensation  be  desire  or  action,  our  theory  still  maintains 
its  superiority.     Let  us  however  try  to  exhibit  this  in  detail. 

What  is  the  fact  to  be  explained  >  It  is,  I  think,  this. 
A  sensation  Ad  has  once  led  to  an  action  Cd ;  and  now  a 
sensation  Ed  (the  same  with  A  in  respect  of  d)  is  presented. 
"Ed  is  then  followed  by  an  action  Fd,  which  in  respect  of  d  is 
identical  with  Cd.  Such  is  the  fact,  and  we  have  two  com- 
peting explanations.  On  the  first  and  incorrect  interpretation 
E^  calls  up  a  particular  image  of  Ad.  The  latter  is  associated 
with  the  particular  idea  of  an  action  Cd,  and  Cd  produces  Fd. 
The  transition  is  thus,  Fb-Ab-Cd-Fd ;  and  this  transition  is 
discrete  from  atom  to  atom.  This  is  the  first  interpretation. 
On  the  other,  Fb  directly  redintegrates  d,  and  Fbd  directly 
produces  FbdF.  The  transition  may  be  stated  as  Fb-d-F  ; 
but,  since  b  and  d  are  universals  and  are  not  psychical 
phenomena,  the  actual  transition  is  unbroken  from  E  to  F. 
Now  which  of  these  explanations  accords  best  with  fact } 
The  fact  is  that  the  supposed  intermediate  units,  Ab  and 
Cd,  can  not  be  verified  in  observation.  Their  presence  is 
deduced  a  priori,  and  is  not  pointed  out  a  posteiHori.  We  are 
then  asked  to  believe  that  their  presence  exists  though  we 
can  not  see  it ;  for  it  is  hidden  by  the  Laws  of  Obliviscence. 
But  this  mysterious  agency  has  itself  been  manufactured  a 
priori.  It  again  can  not  be  verified  in  actual  experience. 
Hence  we  have  first  a  principle  which  produces  something 
other  than  our  fact,  and  then  an  arbitrary  invention  to  patch 
up  this  mistake.  Such  is  the  first  interpretation  ;  and  let  us 
look  at  the  second.  On  that,  I  will  not  say  that  nothing  is 
asserted  either  more  or  less  than  what  can  be  observed,  but  I 
will  say  this.  Not  only  is  one  principle  used  throughout,  and 
that  one  sufficient  to  explain  the  facts,  but  there  is  no  result, 
and  not  the  fraction  of  a  phenomenon,  postulated  by  this 
principle,  but  what  can  be  shown  a  posteriori.  And,  even 
apart   from    all    question    of  truth    and  falsehood,    a   theory 


286  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  II. 

which  demands  two  compensating  hypotheses,  must  surely 
be  rejected  in  favour  of  a  theory,  which  works  as  well  with 
one  single  hypothesis. 

§  13.  But  I  shall  be  told,  "This  statement  of  the  case  is 
absurd.  In  the  first  place,  and  apart  from  truth  and  false- 
hood, the  theory  you  advocate  does  not  cover  the  facts.  It 
fails  to  explain  the  suggestion  of  similars.  Again  and  in 
the  second  place,  the  hypothesis  you  adopt  is  demonstrably 
false.  And  a  single  hypothesis  is  not  admissible  if  it  is 
insufficient,  if  it  is  not  true,  and  if  a  true  explanation  is 
within  our  reach.  I  answer.  In  the  first  place,  as  I  shall 
soon  point  out,  the  reduction  of  suggestion  to  redintegration 
is  an  accomplished  fact.  And  in  the  second  place  the 
falsity  of  redintegration  can  not  be  shewn  ;  but  on  the  other 
hand  what  can  be  demonstrated  is,  that  your  hypothesis  is 
false.  For  (i)  there  is  no  such  thing  as  Association  by 
Contiguity  ;  (ii)  there  is  no  such  thing  as  Association  by 
Similarity.  I  will  try  to  make  both  of  these  last  points  quite 
plain,  and  will  then  return  to  defend  the  true  explanation. 

§  14.  (i)  Let  us  begin  with  Contiguity.  What  is  the  true 
view  }  The  true  doctrine  is  that,  when  elements  have  co- 
existed, they  tend  to  be  connected.  What  does  this  mean  .? 
It  means  that  if  (say)  in  a  perception  A  the  elements  fi  and 
7  are  conjoined,  the  mind  gets  a  tendency  to  join  one  to  the 
other  whenever  either  reappears.  But  what  are  /9  and  7  ? 
They  are  universals.  They  have  been  detached  from  their 
original  environment,  and  to  some  extent  stripped  of  their 
particular  qualities.  They  are  not  individual  images.  Thus 
if  I  have  seen  a  black  man  stabbed  with  a  sword  in  a  certain 
street  at  a  certain  time  and  under  certain  conditions,  what  is 
left  in  the  mind  is  not  a  connection  between  these  special 
sensations,  or  between  special  images  which  are  their  feebler 
counterparts.  I  might  shudder  when  I  saw  a  white  cow 
threatened  with  a  butcher's  knife  at  another  time  and  place 
and  under  different  conditions.  For  what  is  associated  is  not 
the  images,  it  is  always  universals  or  types,  which  as  such 
have  no  real  existence,  even  in  the  mind.  This  is  the  true 
view.  We  will  pass  to  the  consideration  of  the  erroneous 
doctrine. 


Chap.  I.]      THE   THEORY  OF   ASSOCIATION   OF   IDEAS.  28/ 

There  is  not  much  doubt,  I  think,  what  that  doctrine 
really  is.  But  its  adherents  allow  themselves  a  looseness  of 
statement  which  is  sometimes  excessive  ;  and  we  hardly  know 
the  point  at  which  their  mythology  becomes  conscious.  We 
are  at  times  led  to  think  that  past  perceptions  continue  to 
exist,  and  on  occasion  rise  to  be  seen  of  men.  For  observe 
the  definition. 

"Actions,  Sensations,  and  States  of  Feeling,  occurring 
together  or  in  close  succession,  tend  to  grow  together,  or 
cohere,  in  such  a  way  that,  when  any  one  of  them  is  after- 
wards presented  to  the  mind,  the  others  are  apt  to  be  brought 
up  in  idea."  "  When  two  impressions  have  been  frequently 
experienced  (or  even  thought  of)  either  simultaneously  or  in 
immediate  succession,  then  whenever  one  of  these  impressions, 
or  the  idea  of  it,  recurs,  it  tends  to  excite  the  idea  of  the 
other." 

A  definition  is  not  the  place  where  one  looks  for  fancy,  but 
for  actual  belief  But  consider  these  phrases,  "  when  any  one 
of  them  is  aftei'wards  presented^'  "  zvhenever  one  of  these  im- 
pressions recuj'sT  Are  they  feasible  unless  the  writer  believes 
in  the  coarsest  form  of  subterranean  existence  and  of  the 
Resurrection  of  the  body  ?  But  neither  of  the  writers  professes 
to  hold  that  belief  They  both  repudiate  it.  And  yet  that 
does  not  prevent  both  of  them  from  speaking  as  if  they 
accepted  it  in  full,  and  at  least  one  of  them  from  reasoning  on 
the  assumption  of  its  truth.* 

§  15.  This  point  perhaps  may  be  dismissed  as  a  mere 
question  of  statement ;  for  there  is  no  doubt  that  our  authors 
would  stoutly  deny  that  the  past  impression  is  recalled  to 
life.  "  Whenever  one  of  these  impressions,  or  the  idea  of  it, 
recurs "  are  words  that  must  be  used  in  a  popular  sense. 
Then  what  is  the  exact  sense  }  Are  we  to  amend  the  formula 
by  writing  simply,  "  whenever  the  idea  of  one  of  these  im- 
pressions recurs  "  ? 

Even   so   we   are   still   in  the  land  of  mythology.     The 

"  ideas "    that    are    meant    are    particular   existences.     The 

fleeting  impressions  in  their  passage  through  the  void  throw 

off  feebler   counterparts,   shed    pale  doubles   of  themselves. 

*  I  refer  to  J.  S.  Mill.     See  his  Hamilton^  Chap.  XI.  and  Appendix. 


288  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  H. 

And  the  idea,  like  the  impression,  is  a  particular  unit,  it  is  no 
universal  but  an  actual  phenomenon.  It  certainly  is  called 
"the  idea  ^/ the  impression,"  but  this  phrase  does  not  mean 
that  the  two  have  any  substantial  identity.  It  means  that 
one  follows  the  other  in  time,  and  in  fainter  traces  shows  a 
similar  detail.  But  if  this  is  what  is  meant,  it  is  not  what 
is  said. 

"  Whenever,"  we  are  told,  "  the  idea  of  it  recurs!'  But  the 
idea,  like  the  impression,  exists  only  for  a  moment.  Then 
how  can  it  "  recur  "  unless  it  is  the  same  ;  and  how  can  it  be 
the  same  unless  it  has  remained  .-*  We  may  figure  to  ourselves 
the  faithful  ghost,  haunting  the  place  where  the  body  is  not, 
and  called  up  to  the  light  by  the  spell  of  Association.  But 
we  surely  must  know  that  these  pious  legends  are  not  literally 
true.  For  the  image,  like  the  sensation,  endures  but  for  a 
moment.  And  if  the  impression  does  not  "  recur,"  then  the 
idea  does  not  "  recur ; "  since  in  this  respect  there  is  no 
difference  between  them. 

It  is  mere  mythology  to  talk  of  the  copy,  which  the  im- 
pression has  sloughed  ofT,  persisting  in  the  world  and  preserving 
its  identity  through  the  flux  of  change.  The  word  recurs  must 
be  struck  out  of  the  formula.  There  are  a  train  of  images, 
there  is  not  one  image.  And  with  this  fable  must  depart 
another  loose  phrase.  We  have  no  right  to  call  a  broken 
procession  of  several  images,  "  the  idea  of  an  impression."  We 
must  call  them  "  different  ideas  of  the  impression."  And  here, 
I  think,  we  are  approaching  danger.  For  we  naturally  consider 
that,  in  a  case  of  association,  there  is  some  one  connection 
throughout  all  the  instances.  We  can  hardly  help  believing, 
and  talking  as  if  we  believed,  that  when  (as  we  should  like  to  say) 
something  "  recurs,"  then  something  else  "  recurs  "  also.  But 
we  must  strip  off  this  illusion,  or  wear  it  only  when  we  come 
before  the  public.  There  is  nothi7ig  that  recurs.  The  original 
impression  is  one  mental  unit,  the  first  idea  is  another,  the 
second  idea  is  a  third  passing  atom,  and  so  on  for  ever.  There 
is  no  real  bond  which  unites  them  together.  There  is  no 
common  internal  identity,  which  is  the  same  in  all  and  recurs 
amid  change.  If  we  call  them  "  the  ideas  of  one  impression," 
even  this  is  mere  fable.     We  have  a  likeness  no  doubt,  in  all 


Chap.  L]      THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  289 

these  cases.  A  hundred  images,  or  more  it  may  be,  with  all 
their  differences  and  all  their  particularity,  are  yet  each  of 
them  particular  in  such  a  way  that  they  are  all  like  each  other, 
and  all  like  the  impression.  This  is  startling,  I  admit,  but 
even  this  does  not  warrant  us  in  considering  any  one  to  be  the 
same  as  the  other,  and  united  by  holding  the  one  substance  of 
their  prototype.  If  we  desire  a  legend  which  perhaps  may  be 
harmless,  we  may  call  them  all  "  ideas  of  the  impression  "  in 
the  sense  that,  like  Abraham,  the  impression  while  it  lived  had 
them  all  in  its  loins.  For  no  vehicle  conveys  the  eternal  verities 
half  so  well  as  does  the  labyrinth  of  a  fantastic  genealogy, 
with  its  one-sided  begettings  and  abnormal  parturition. 

§  16.  "  Whenever  one  of  these  impressions,  or  the  idea  of  it, 
recurs,  it  tends  to  excite  the  idea  of  the  other."  This  is  what 
we  started  from.  What  are  we  left  with  }  "  Impressions  "  is 
gone  :  "  recurs  "  is  gone  :  "  idea  of  it "  is  gone.  It  seems  that 
we  must  thus  amend  our  formula,  "Whenever  an  idea  like 
one  of  these  impressions  occurs,  it  tends  to  excite  the  idea  of 
the  other."  This  surely  will  stand  :  this  at  last  must  be  true. 
Unfortunately  not  so  ;  for  it  still  says  too  much  and  must  be 
further  cut  down  ;  and  yet  already  it  has  begun  to  say  too 
little,  and  will  now  no  longer  cover  the  facts.  But  I  will  at 
present  keep  to  the  too  much.  The  phrase  "  to  excite  the 
idea  of  the  other  "  must  at  once  be  corrected.  It  should  run 
"to  excite  an  idea  like  the  other."  And  we  must  further 
amend  the  beginning  of  our  formula.  For  "  when  two  impres- 
sions have  been  frequently  experienced  "  is  quite  mythological. 
If  two  impressions  were  "  frequently  experienced,"  they 
would  be  two  no  longer.  The  phrase  is  nonsensical,  unless 
several  experiences  are  one  experience  :  and  that  we  know  is 
not  true.  We  must  alter  this  also,  and  in  our  final  correction 
the  law  must  be  stated. 

"  When  we  have  experienced  (or  even  thought  of)  several 
pairs  of  impressions  (simultaneous  or  successive),  which  pairs 
of  impressions  are  like  one  another ;  then  whenever  an  idea 
occurs  which  is  like  all  the  impressions  on  one  side  of  these 
pairs,  it  tends  to  excite  an  idea  which  is  like  all  the  impressions 
on  the  other  side." 

This  I  believe  to  be  the  meaning  of  Association  by  Contiguity. 


290  THE   PRINCIPLES   OF  LOGIC.  [Bk.  IL  Pt.  II 

And  at  this  point  perhaps  it  may  occur  to  us  to  ask,  what  is  it 
that  is  contiguous,  and  what  is  it  that  is  associated  ?  The 
impressions  are  not  associated ;  I  presume  that  is  obvious. 
They  are  conjoined  in  presentation,  just  like  anything  else  we 
perceive  together  is  conjoined.  It  is  the  ideas  which  are 
associated,  since  one,  as  we  see,  can  bring  up  another.  But 
then  in  what  sense  are  the  ideas  contiguous  ?  They  are  now 
successive,  or  simultaneous,  because  of  the  contiguity.  Con- 
tiguity conjoins  them,  and  it  would  be  nonsense  to  say  that 
they  become  conjoined  because  already  they  are  contiguous. 
For  if  they  are  contiguous,  then  both  must  be  there,  and  how 
can  one  call  in  the  other  t  And  if  they  are  not  contiguous, 
then  it  is  not  their  contiguity  which  brings  them  together. 
This  consideration  seems  to  me  quite  palpable  ;  but  the  result 
is  fatal  to  the  Law  of  Contiguity. 

The  law  operates  by  means  of  and  through  contiguity,  and 
therefore  presupposes  it.  But  there  is  no  contiguity  save  that 
of  the  impressions.  It  must  be  then  the  contiguity  of  the 
impressions  which  works.  Because  they  were  together  once, 
the  ideas  come  together  now.  But,  if  so,  what  becomes  of  the 
association  }  For  the  impressions  are  not  associated,  and  the 
association  is,  if  anywhere,  between  a  present  and  an  absent 
idea.  What  is  associated  was  therefore  not  contiguous,  and 
what  was  contiguous  is  now  not  associated.  Association  and 
contiguity  fall  hopelessly  asunder  ;  and  hence  let  our  law  be 
never  so  real,  it  can  not  be  the  Law  of  Association  by  Contiguity. 
In  short,  the  whole  thing  comes  to  this.  If  impressions  have 
been  contiguous,  then  ideas  which  are  like  them  now  tend  to 
excite  one  another.  And  for  myself,  I  can  not  see  how  in  any 
intelligible  sense  this  is  the  association  of  ideas. 

§  17.  And  now  (to  come  to  the  other  side  of  the  failure)  if 
we  state  the  law  in  this  corrected  form,  it  will  not  cover  the 
facts  of  the  case.  For  commonly  an  impression  is  what  is  first 
given,  and  then  this  impression  calls  up  an  idea.  Thus  if  one 
fire  has  already  been  felt  to  be  hot,  then,  if  another  fire  is  seen^ 
the  idea  heat  comes.  Thus  an  idea  is  excited  by  what  is  not 
an  idea,  and  by  what  never  has  been  contiguous  to  anything. 
We  must  once  more  and  finally  thus  amend  our  formula, 
*'If  any  mental  units  have  been  contiguous,  then  any  others 


Chap.  I.]      THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  29 1 

which  resemble  them  may  excite  one  another."  There  is  not 
left  here  a  vestige  of  association.  And  the  union  of  the  elements 
somehow  takes  place  by  virtue  of  the  past  contiguity  of  some- 
thing else. 

§  1 8.  Association  by  contiguity  may  be  taken  as  exploded. 
But  the  philosophy  of  Experience  is,  to  some  extent  at  least, 
prepared  for  this  result.  It  will  admit  so  much,  that  mere 
contiguity  will  not  work  by  itself.  And  it  proposes  to 
support  it  by  another  agent.  There  is  no  such  thing,  it  is 
ready  to  allow,  as  association  by  bare  contiguity.  All  re- 
production in  a  certain  sense  depends  on  similarity. 

"  There  never  could  have  been  association  by  contiguity 
without  a  previous  association  by  resemblance.  Why  does  a 
sensation  received  this  instant  remind  me  of  sensations  which 
I  formerly  had  (as  we  commonly  say),  along  with  it  ?  I 
never  had  them  along  with  this  very  sensation.  I  never  had 
this  sensation  until  now,  and  can  never  have  it  again.  I  had 
the  former  sensations  in  conjunction  not  with  it,  but  with  a 
sensation  exactly  like  it.  And  my  present  sensation  could 
not  remind  me  of  those  former  sensations  unlike  itself,  unless 
by  first  reminding  me  of  the  sensation  like  itself,  which  really 
did  co-exist  with  them.  There  is  thus  a  law  of  association 
anterior  to,  and  presupposed  by,  the  law  of  contiguity : 
namely,  that  a  sensation  tends  to  recall  what  is  called  the 
idea  of  itself,  that  is,  the  remembrance  of  a  sensation  like 
itself,  if  such  has  previously  been  experienced."  "  There  is, 
therefore,  a  suggestion  by  resemblance — a  calling  up  of  the 
idea  of  a  past  sensation  by  a  present  sensation  like  it — which 
not  only  does  not  depend  on  association  by  contiguity,  but  is 
itself  the  foundation  which  association  by  contiguity  requires 
for  its  support."     J.  S.  Mill,  071  James  Mill,  I.  112,  113. 

"  There  can  be  no  contiguity  without  similarity,  and  no 
similarity  without  contiguity.  When,  looking  at  a  river,  we 
pronounce  its  name,  we  are  properly  said  to  exemplify 
contiguity ;  the  river  and  the  name  by  frequent  association 
are  so  united  that  each  recalls  the  other.  But  mark  the  steps 
of  the  recall.  What  is  strictly  present  to  our  view  is  the 
impression  made  by  the  river  while  we  gaze  on  it.  It  is 
necessary  that  this  impression  should,  by  virtue  of  similarity 

U  2 


292  .  THE   PRINCIPLES  OF  LOGIC.  [Bk.  IL  Pt.  II. 

or  identity,  re-instate  the  previous  impression  of  the  river,  to 
which  the  previous  impression  of  the  name  was  contiguous. 
If  one  could  suppose  failure  in  the  re-instatement  of  the 
former  idea  of  the  river,  under  the  new  presentation,  there 
would  be  no  opportunity  given  to  the  contiguous  bond  to 
come  into  operation."     Bain,  ibid.  p.  121. 

Let  us  try  to  understand  this  amended  doctrine.  In  the 
first  place  we  must  remember  that,  when  identity  is  spoken  of, 
it  is  not  really  meant.  What  is  meant  is  more  or  less  of 
similarity.     And  this  point  must  not  be  lost  sight  of 

In  the  second  place  I  must  be  allowed  to  complain  of  a 
serious  inaccuracy  in  the  extract  I  have  quoted  from  Professor 
Bain.  It  surely  is  nonsense  to  talk  of  "re-instating  the 
previous  impression,"  and  I  must  add  that  in  this  context 
the  nonsense  seems  inexcusable.  And  again  in  the  first  of  the 
extracts  there  is  ambiguity.  The  "  remembrance  of  a  sen- 
sation," we  must  clearly  understand,  does  not  revive  the 
sensation  itself,  and  does  not  establish  any  actual  relation 
with  that  mental  unit  which  no  longer  exists.  If  this  is  not 
so,  and  if  a  psychical  phenomenon  can  maintain  or  recover  its 
existence  and  identity  through  the  flux  of  events,  then  the 
whole  theory  from  which  the  school  of  Association  starts  has 
been  tacitly  thrown  over. 

But,  if  an  impression  when  past  is  done  with,  if  it  is  really 
non-existent,  then  not  only  can  it  not  be  re-instated  bodily, 
but  itself  can  not  even  be  re-instated  in  idea.  The  fact  which 
is  covered  by  the  delusive  phrase  "  idea  of  it,"  is  merely  the 
fact  that  a  sensation  came  first,  and  then  subsequently  there 
came  a  paler  counterpart.  And,  when  we  once  discern  this 
fact  through  the  mist  of  ambiguous  and  misleading  formulae, 
there  is  an  end  to  the  theory  which  hides  or  obscures  it. 

What  was  contiguous  is  now  non-existent,  and  what  is 
"  re-instated  "  has  never  been  contiguous.  Let  us  look  at  the 
facts.  A  sensation  A  excites  by  similarity  an  image  b,  and, 
on  this,  contiguity  has  to  do  all  the  rest.  But  has  b  ever  been 
contiguous  to  anything  ?  In  the  case  before  us  there  are  two 
possibilities.  The  fact  from  which  we  start  is  this — we  have 
had  an  impression  B  along  with  an  impression  C,  and  we 
have  an  impression  A.     Now  what  are  the  two  possibilities? 


Chap.  I.]      THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  293 

In  the  first  place  it  is  possible  that  we  never  have  had  a  feeble 
image  resembling  B.  And  this  is  more  than  possible,  for  in  an 
early  mind  it  is  also  probable.  But  in  this  case,  when  A 
excites  an  image  b,  there  is  absolutely  no  contiguity  of  any- 
thing with  anything.  Not  one  of  the  supposed  elements  in 
our  reproduction  has  ever  been  contiguous  with  any  other ; 
and,  this  being  so,  reproduction  will  not  take  place.  This 
first  possibility  appears  to  me  to  have  been  overlooked.  Let 
us  now  pass  to  the  second.  We  here  have  had  the  contiguous 
impressions  B  —  C.  These  we  suppose  to  have  been  followed 
by  one  or  more  pale  pairs  of  images  b^  —  c^,  b'^  —  c^,  b'^  —  c^. 
These  are  all  like  each  other,  but  they  all  are  realities  each  of 
which  is  not  the  same  as  any  other.  We  now  experience  a 
sensation  A.  This  also  is  like  the  previous  sensation  we  have 
called  B,  and  is  like  the  images  b^,  b"-,  b^.  But  every  one  of 
these,  I  must  b§g  the  reader  to  remember,  is  by  this  time 
absolutely  non-existent.  What  then  is  to  happen  when  A  is 
presented  ?  It  calls  up  by  similarity  an  image  b^.  But  this 
is  not  what  we  want.  For  we  want  an  image  b^  —  c^',  and 
contignity  is  invoked  to  present  us  with  c^.  But  is  invoked  in 
vain.  For  as  yet  d^  has,.never  existed,  and  ex  hypothesi  it  is  to 
be  made  to  exist  by  means  of  contiguity.  On  the  other  hand 
b^  has  never  been  contiguous  to  anything  at  all.  We  have 
reached  once  again  the  old  result.  There  is  no  association 
by  contiguity.  What  is  called  up  by  association  has  never 
been  contiguous  ;  and  what  has  been  contiguous  can  not  be 
called  up.  The  contiguity  which  now  operates  is  a  past 
contiguity,  which  is  not  recalled  and  can  not  be  recalled,  but 
which,  according  to  the  pious  legend,  is  somehow  passed  on 
like  original  sin. 

But  if  this  is  so,  then  Association  by  Contiguity  is  ex- 
ploded finally.  No  exciting  of  similars  will  save  it  from 
annihilation.  For  the  similars  excited  have  not  been  conti- 
guous, and  what  was  really  contiguous  can  not  be  excited. 
If  present  sensations  are  qualified  by  images  in  the  way 
described,  still  on  that  (false)  hypothesis  there  is  no  repro- 
duction by  association.  There  can  be  no  association  where 
the  elements  are  not  co-existing  associates.  But  if  they  do 
already  co-exist  and  thus  are  associated,  then  how  in  the  name 


294  THE   PRINCIPLES   OF  LOGIC.  [Bk.  II.  Pt.  II. 

of  all  that  is  miraculous  can  one  bring  about  the  co-existence 
of  the  other,  and  by  means  of  their  co-existence  ? 

§  19.  If  the  school  of  Experience  is  in  earnest  with  its 
principles  there  can  be  no  such  thing  as  Association.  But  is 
it  in  earnest  ?  Notwithstanding  all  its  public  protestations 
may  it  not  secretly  look  for  the  Resurrectfon  of  the  Body  ? 
Does  not  the  charm  of  Similarity  shake  the  realm  of  Hades, 
and  conjure  from  its  grave  the  reluctant  past  ?  Is  anything 
too  hard  for  Association  ?  Its  spell  has  prevailed  over  the 
mind  of  its  votaries,  and,  though  their  lips  may  deny,  yet 
Association  itself  has  helped  their  unbelief  by  its  own  divine 
power.  They  do  believe  in  the  miracle  of  resurrection.  But 
they  believe  blindly  and  unconsciously,  compelled  by  the 
strength  of  a  tacit  conjunction  of  meaning  with  phrase. 

We  saw  that,  by  the  admission  of  its  advanced  disciples, 
association  depends  upon  [similarity.  If  there  is  no  repro- 
duction by  Similarity,  it  is  admitted  that  there  is  no  Associa- 
tion at  all,  I  shall  now  press  this  consequence.  If  you  do 
not  believe  in  this  kind  of  Association,  you  believe  in  none. 
But  if  you  do  believe  in  it  you  believe  in  a  miracle  which 
upsets  all  law.  And  furthermore  there  is  no  evidence  a 
posteriori  to  confirm  this  miracle.  In  plain  words  Association 
by  Similarity  is  a  downright  fiction.  It  is  not  called  for  by 
the  facts  ;  and  it  involves  besides  metaphysical  assumptions 
which  I  confess  stagger  me,  and  which  I  think  may  somewhat 
surprise  others.  I  shall  show  the  reader  how  the  school 
of  Experience  has  swallowed  the  most  outrageous  meta- 
physical doctrines,  and  that  he  must  follow  their  example  or 
leave  their  company. 

§  20.  (ii)  Association  by  similarity,  if  it  is  anything  at  all, 
is  a  means  of  exciting  ideas  that  are  not  present.  If  it  will 
not  give  us  what  at  present,  and  apart  from  its  agency,  we  are 
without,  then  it  surely  is  a  self-condemned  fiasco,  that  is  not 
worth  discussing.  We  may  perhaps  agree  that  an  agency 
which  recalls  and  yet  recalls  not  anything  but  what  is  already 
on  the  spot,  is  something  like  a  piece  of  nonsense.  And  I 
propose  to  show  that  Association  by  Similarity  is  this  piece 
of  nonsense. 

Similarity  is  a  relation.     But  it  is  a  relation  which,  strictly 


Chap.  L]     THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  295 

speaking,  does  not  exist  unless  both  terms  are  before  the 
mind.  Things  may  perhaps  be  the  same  in  certain  points 
although  no  one  sees  them ;  but  they  can  not  properly 
resemble  one  another,  unless  they  convey  the  impression  of 
resemblance  ;  and  they  can  not  convey  it  unless  they  are 
both  before  the  mind.  This  is  not  merely  an  assertion  I  have 
chosen  to  make.     Let  us  see  what  is  told  us  by  J.  S.  Mill. 

"Any  objects,  whether  physical  or  mental,  are  related,  or 
are  in  a  relation,  to  one  another,  in  virtue  of  any  complex 
state  of  consciousness  into  which  they  both  enter  "  {o7t  James 
Mill,  II.  10). 

"  Likeness  and  unlikeness  are  themselves  only  a  matter  of 
feeling :  and  that  when  we  have  two  feelings,  the  feeling  of 
their  likeness  or  unlikeness  is  inextricably  interwoven  with 
the  fact  of  having  the  feelings.  One  of  the  conditions,  under 
which  we  have  feelings,  is  that  they  are  like  and  unlike  :  and 
in  the  case  of  simple  feelings,  we  can  not  separate  the  like- 
ness or  unlikeness  from  the  feelings  themselves.  It  is  by  no 
means  certain,  however,  that  when  we  have  two  feelings  in 
immediate  succession,  the  feeling  of  their  likeness  is  not  a 
third  feeling  which  follows  instead  of  being  involved  in  the 
two"  {ibid.  p.  18). 

"  I  have  two  sensations  ;  we  will  suppose  them  to  he 
simple  ones  ;  two  sensations  of  white,  or  one  sensation  of 
white  and  another  of  black.  I  call  the  first  two  sensations 
like ;  the  last  two  unlike.  What  is  the  fact  or  phenomenon 
constituting  the  fundamentum  of  this  relation  1  The  two 
sensations  first,  and  then  what  we  call  a  feeling  of  resem- 
blance, or  of  want  of  resemblance.  Let  us  confine  ourselves 
to  the  former  case.  Resemblance  is  evidently  a  feeling ;  a 
state  of  the  consciousness  of  the  observer"  (Logic,  I.  75). 

Is  not  this  quite  plain  ?  Does  it  leave  any  doubt }  Is  it 
not  clear  that  two  mental  elements  are  not  like,  unless  I  have 
them  before  me  at  once  or  in  immediate  succession  >  But,  if 
so,  what  meaning  can  we  attach  to  the  calling  up  of  an  idea 
by  similarity  ?  If  the  relation  does  not  exist  until  the  idea  is 
called  up,  how  can  the  idea  be  called  up  by  the  relation  }  Is 
it  not,  the  moment  we  look  below  the  surface,  mere  verbiao-e 
and  nonsense  ? 


296  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  II. 

§  21.  In  the  first  place  what  is  called  up  is  absolutely 
non-existent.  We  are  told,  not  once  but  again  and  again, 
that  a  feeling  gone  is  gone  for  ever.  And  the  same  thing 
holds  of  particular  images.  If  these  exist,  then  the  past 
exists,  and  the  procession  in  the  mind  is  not  real  but  illusory. 
Are  we  to  believe  this,  and  believe  it  in  the  teeth  of  our 
asseverations  ?  But  if  we  can  not  believe  it,  and  if  the 
past  does  not  exist,  then  we  must  believe  in  a  relation 
between  the  existent  and  the  non-existent ;  and  believe  that 
the  whole  (relation  and  relateds)  is  one  state  of  our  minds. 
If,  on  the  other  hand,  the  past  can  exist,  this  miracle  will  not 
save  us  from  annihilation.  In  the  relation  of  similarity  both 
terms  must  be  present,  and  the  fact  that  one  calls  up  the 
other  by  this  relation,  postulates  that  one  of  the  terms  must 
be  absent.  It  is  therefore  both  present  and  absent  at  once. 
On  either  hypothesis  we  are  landed  in  contradictions  ;  and  I 
have  redeemed  the  promise  I  gave  to  the  reader.  An  idea 
is  absent  and  at  the  same  time  present.  It  is  not  there  and 
so  is  brought  in  by  a  relation,  which  relation  is  nothing  if  the 
idea  is  not  there.  And  a  union,  which  is  impossible  out  of 
the  mind,  persists  between  the  existent  and  what  is  wholly 
non-existent.  Could  anything  be  more  insane  than  this  wild 
metaphysic } 

§  22.  But  I  shall  be  told  "  You  are  deceiving  us ;  it  is 
incredible,  it  is  impossible  that  our  sober  countrymen  can 
have  been  so  imposed  upon."  I  answer.  That  question  is 
easily  settled.  It  is  admitted  that  by  "  association  "  they 
must  mean  something,  and  what  else  do  they  mean  } 

The  Experience  Philosophy  has  to  meet  two  objections. 
It  has  to  explain  how  the  non-existent  can  be  related  to  the 
existent.  And  when  it  has  done  that,  it  must  explain  how 
the  absent  can  be  recalled  by  the  present,  when  similarity 
implies  common  presence  and  reproduction  excludes  it. 
Suppose  that  the  former  difficulty  has  been  slurred  over  by 
some  metaphysical  formula  of  "  the  potential  and  the  actual," 
or  some  distinction  between  7ny  mind  and  other  minds,  yet 
the  second  remains.  Suppose  that  your  past  series  somehow 
exists,  yet  how,  I  ask,  are  you  going  to  get  at  it }  Mere 
partial  identity  of  the  present  and  the  past  would  not  be 


Chap.  I.]     THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  297 

what  you  want,  since  this  would  not  be  an  actual  relation  m 
your  mi  fid. 

This  is  what  Maas  meant  by  the  following  objection. 
*'  The  mere  similarity  of  two  ideas  (or  sensations)  can  not 
possibly  be  a  cause  of  their  association.  For  similarity  is  an 
objective  relation  of  the  ideas  themselves  ;  while  association 
is  a  subjective  connection  in  the  imagination.  But  the  latter 
does  not  follow  from  the  former,  nor  tend  to  follow  from  it " 
{Ve7'such,  p.  55).  By  "similarity  "  Maas  of  course  here  meant 
"partial  identity,"  and  his  argument  is  quite  simple.  The 
question  is,  Why  does  my  mind  go  from  one  element  to 
another }  If  you  say,  it  goes  because  the  elements  see7n  like 
to  it — that  supposes  both  to  be  there.  But  if  you  say,  it  goes 
because  they  a?'e  like  apart  from  it — then  it  goes  by  a  miracle, 
for  it  is  influenced  by  something  which  to  it  is  nothing. 
Sir.  W.  Hamilton  {Reid,  p.  914)  has  replied  to  this  argument 
by  a  criticism  which  shows  that  he  did  not  understand  it. 

The  Experience  Philosophy  may  have  a  reply  to  these 
objections,  but  I  confess  I  can  not  anticipate  its  answer. 
Perhaps  it  may  fall  back  on  a  simpler  view.  It  may  say, 
after  Wundt  (Phys.  Psych.  ^'^'S),  "every  perception  or  idea 
tends  to  call  into  consciousness  another  like  itself."  As  to 
the  truth  of  this  expression  I  shall  have  something  to  say 
afterwards.  But  at  present  I  say  this.  Whatever  else  it  is, 
it  is  giving  up  Association  and  throwing  it  overboard.  For  it 
is  the  mere  statement  of  a  phenomenon  ;  and  it  is  not  an 
explanation.  The  entirest  belief  in  the  truth  of  this  formula 
is  compatible  with  the  entirest  disbelief  in  the  doctrine  of 
Association.  We  might  explain  the  alleged  fact  that,  given 
any  one  element,  another  like  it  may  come  up,  by  a  theory 
of  the  spontaneous  fission  or  gemmation  of  ideas  ;  and  this  in 
my  opinion  would  be  a  theory  which,  by  the  side  of  Associa- 
tion, is  sober  and  rational.  We  might  explain  it  again  by  a 
physiological  disposition  to  a  certain  cerebral  function,  which 
(given  the  stimulus  of  a  new  perception  or  idea)  passes  into 
fact.  And  against  this  explanation  I  will  not  say  one  word. 
I  will  insist  only  on  this,  that  it  is  not  a  psychological  explana- 
tion at  all,  and  that  in  the  hands  of  those  who  know  their 
own  business  it  is  not  offered  as  such.     If  this  is  the  only 


298  ,    THE   PRINCIPLES  OF   LOGIC.  [Bk.  IL  Pt.  IL 

possible  explanation,  then  a  psychological  explanation  is 
relinquished  as  impossible,  and  the  Laws  of  Association  as 
commonly  given  will  not  explain  anything.  Thus  the 
Philosophy  of  Experience  must  take  its  choice.  It  must 
either  rehabilitate  its  barbarous  mythology,  or  admit  that, 
though  the  fact  of  reproduction  is  known,  it  has  no  psycho- 
logical explanation  to  offer,  and  is  confessedly  bankrupt. 
It  has  rested  its  all  on  reproduction  by  similarity,  and  we 
have  shown  that  this  is  an  impossibility. 

§  23.  But  our  proof  no  doubt  will  not  cause  much  disquiet. 
I  shall  be  told  "You  can  not  demonstrate  away  the  facts." 
And  I  will  therefore  proceed  to  my  second  contention.  The 
explanation  offered  is  not  only  impossible,  but  it  is  also 
uncalled  for.  There  is  no  evidence,  for  it  a  posteriori.  The 
facts  of  reproduction  are  much  better  explained  on  another 
theory.  We  have  seen  this  already  in  our  first  Book,  but  I 
will  exhibit  it  once  more. 

Let  us  take  a  fairly  simple  instance  of  reproduction.  A 
young  child,  or  one  of  the  lower  animals,  is  given  on 
Monday  a  round  piece  of  sugar,  eats  it  and  finds  it  sweet. 
On  Tuesday  it  sees  a  square  piece  of  sugar,  and  proceeds  to 
eat  it.  In  this  we  have  of  course  volitional  phenomena  as 
well  as  intellectual,  but  perhaps  we  may  simplify  the  case  so 
as  to  make  it  serve. 

Now  on  the  Association  theory  how  is  the  fact  interpreted  ? 
I  suppose  in  some  way  like  this.  The  presentation  to  the 
eye  of  Tuesday's  piece  calls  up  by  similarity  the  idea  of 
Monday's  piece.  That  is  a  feeble  counterpart  of  the  original 
sensation,  and  it  calls  up  by  contiguity  feeble  counterparts  of 
Monday's  felt  movements  and  Monday's  following  sweet  taste. 
The  fact  which  ensues  is  hence  the  mental  presence  of 
Tuesday's  perceived  square  piece,  felt  to  be  like  another 
paler  imagined  round  piece,  with  which  latter  a  whole  set  of 
other  images  come  in.  Now  the  conclusion,  at  which  we  have 
to  arrive,  is  the  qualification  of  Tuesday's  piece  by  these 
images  which  are  attendant  on  the  idea  of  Monday's  piece  ; 
and  at  first  sight  there  seems  no  way  to  this  result.  For  the 
conclusion  is  not  merely  a  vicious  inference,  but  it  does  not 
even  look  like  a  probable  mistake.     Tuesday's  sensation  and 


Chap.  I.]      THE   THEORY  OF  ASSOCIATION   OF  IDEAS.  299 

Monday's  image  are  not  only  separate  facts  which,  because 
alike,  are  therefore  not  the  same  ;  but  they  differ  perceptibly 
both  in  quality  and  environment.  What  is  to  lead  the  mind 
to  take  one  for  the  other  ? 

Sudden  at  this  crisis,  and  in  pity  at  distress,  there  leaves 
the  heaven  with  rapid  wing  a  goddess  Primitive  Credulity. 
Breathing  in  the  ear  of  the  bewildered  infant  she  whispers,  The 
thing  which  has  happened  once  will  happen  once  more. 
Sugar  was  sweet,  and  sugar  will  be  sweet.  And  Primitive 
Credulity  is  accepted  forthwith  as  the  mistress  of  our  life. 
She  leads  our  steps  on  the  path  of  experience,  until  her 
fallacies,  which  can  not  always  be  pleasant,  at  length  become 
suspect.  We  wake  up  indignant  at  the  kindly  fraud  by 
which  the  goddess  so  long  has  deceived  us.  So  she  shakes 
her  wings,  and  flying  to  the  stars,  where  there  are  no 
philosophers,  leaves  us  here  to  the  guidance  of — I  can  not 
think  what. 

The  school  has  not  yet  accepted  this  legend,  and  I  narrate 
partly  because  I  am  not  sure  that  it  is  not  relevant,  but 
mainly  because  it  has  always  seemed  to  me  perhaps  the  most 
striking  of  all  those  creations  which  we  owe  to  the  imagina- 
tion of  Professor  Bain  {Emots.  p.  5  n  and  foil). 

§  24.  The  less  poetical  but  not  less  fabulous  view  would 
appear  to  be  this.  Given  a  perception  A  together  with  an 
image  b,  which  resembles  it  and  has  a  train  of  attendant 
images  c,  d,  and  e — the  problem  is  how  to  transfer  to  A  the 
content  of  e.  And  what  accomplishes  the  feat  is  the  Law  of 
Obliviscence.  This  powerful  agent  obscures  everything  in  the 
train  between  A  and  e ;  and  it  also  obscures  any  part  of  e 
which  is  not  suitable  to  A.  The  residue  of  e  then  adheres  to 
A  ;  that  is,  I  think,  the  two  run  into  one.  And  so  we  get 
the  conclusion  "  This  piece  of  sugar  is  sweet,"  by  a  process 
which  logically  may  seem  rather  vicious,  but  which  appears 
none  the  less  to  be  the  essence  of  reasoning.*      v 

I  can  not  say  if  this  statement  of  the  Association  doctrine 

*  In  the  lowest  stages  of  mind  this  theoretical  conclusion  of  course 
would  not  appear.  There  would  be  action  or  attempt  without  anything 
like  a  judgment.  The  principle  however  would  be  exactly  the  same  ;  and 
when  the  theoretical  conclusion  comes,  it  must  come  in  this  way. 


300  THE  PRINCIPLES  OF  LOGIC.  [Bk.  II.  Pt.  II. 

is  fair,  but  I  hope  it  may  be  so.  Let  us  see  what  objection 
we  can  find  to  its  process. 

The  main  objection  is  that  there  is  a  great  deal  too  much 
of  it.  It  is  much  too  elaborate  for  simple  phenomena.  It 
first  introduces  a  complication  which  does  not  exist ;  and 
then,  having  invented  this  complication,  it  removes  it  by  a 
process  which  is  not  real. 

It  is  obviously  no  fact  which  we  can  discover  by  observa- 
tion, that  when  Tuesday's  sugar  is  presented  to  sense,  a 
similar  piece  or  similar  pieces  come  up,  in  their  particularity 
and  with  all  their  differences,  before  the  mind.  No  one  gets 
such  a  fact  from  observation.  It  is  in  short  a  theoretical 
fiction.  I  do  admit  that  afterwards,  when  memory  is  de- 
veloping, there  is  something  which  can  give  ground  for  a 
mistake  of  this  kind.  But  then  of  course  reproduction  must 
come  before  memory,  and  in  the  present  case  we  are  not 
concerned  with  the  latter  (cf  p.  38).  The  fact  before  the 
mind  is  that  this  sugar  suggests  both  sweetness  and  eating 
without  any  images  of  any  other  pieces  of  sugar  at  all.  In 
the  first  Book  I  enlarged  on  this  point  by  anticipation,  and,  I 
confess,  it  seems  to  me  quite  plain. 

§  25.  But  I  shall  be  told,  that  although  we  can  not  be 
aware  of  them,  these  images  exist,  and  they  are  removed  or 
adapted  by  the  Laws  of  Obliviscence.  But  this  process 
strikes  me  as  another  fiction,  piled  up  to  support  the  first 
fiction  against  the  pressure  of  experience.  I  will  quote  a 
passage  from  J.  S.  Mill. 

"  The  reader  ...  is  now  .  .  .  familiar  with  the  .  .  .  fact,  .  .  . 
that  when,  through  the  frequent  repetition  of  a  series  of  sensa- 
tions, the  corresponding  train  of  ideas  rushes  through  the  mind 
with  extreme  rapidity,  some  of  the  links  are  apt  to  disappear 
from  consciousness  as  completely  as  if  they  had  never  formed 
part  of  the  series.  It  has  been  a  subject  of  dispute  among 
philosophers  which  of  three  things  takes  place  in  this  case. 
Do  the  lost  ideas  pass  through  the  mind  without  conscious- 
ness }  Do  they  pass  consciously  through  the  mind  and  are 
they  then  instantly  forgotten  ?  Or  do  they  never  come  into 
the  mind  at  all,  being,  as  it  were,  overleaped  and  pressed  out 
by  the  rush  of  the  subsequent  ideas  ? "  {on  James  Mill^  I.  106). 


Chap.  I.]     THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  30I 

The  question  opened  in  the  above  quotation  may  be 
stated  thus  :  Given  an  indirect  connection  of  ideas  in  the  mind, 
to  find  the  way  in  which  it  becomes  direct.  I  do  not  wish 
here  to  enter  into  this  general  question.  But  I  must  point 
out  that  Mr.  Mill  has  raised  it  in  a  form  which  precludes 
any  satisfactory  solution.  For  the  ideas  connected  are  not 
really  a  mere  series  of  particular  images,  and  the  fact  has  thus 
been  perverted  beforehand.  And  if  we  suppose  that,  in  some 
exceptional  case,  we  have  got  a  mere  train  of  individual 
images,  then  not  one  of  the  "  three  things  "  could  possibly  be 
operative.  For  so  long  as  the  ideas  remained  these  mere 
images,  no  connection  at  all  would  be  established  between 
them.  We  may  be  sure  that,  whatever  in  the  end  may  be 
the  detail  of  the  psychological  process,  one  side  of  it  would 
consist  in  turning  these  images  into  universals.  And  for  this 
reason  the  Laws  of  Obliviscence,  as  we  have  them  stated  by 
Mr.  Mill,  are  fictitious  processes.  Even  if  you  start  with  a 
complication  and  a  train  of  ideas,  yet  they  can  not  deal 
with  it. 

But  the  point  on  which  I  desire  to  insist,  is  that  in  an 
elementary  case  of  reproduction,  such  as  we  are  now  con- 
sidering, the  complication  presupposed  by  these  Laws  has  no 
existence  at  all.  The  data  from  which  they  start  are  pure 
inventions,  and  it  is  hence  an  impossibility  that  any  one  of  the 
suggested  "  three  things "  should  happen.  The  fact  which 
Obliviscence  postulates  is  this :  A  is  the  sugar  calling  up  by 
similarity  an  image  of  sugar  b ;  and  b  calls  up  by  contiguity 
an  image  of  movement  c ;  and  c  calls  up  an  image  ^  of  a 
particular  sweet  taste.  But  this  fact  does  not  exist,  and  the 
alleged  process  stands  therefore  on  unreality. 

There  is  in  the  first  place  no  reason  to  suppose  that  this 
train  of  ideas,  which  is  presumed  to  rush  through  the  mind,  is 
a  counterpart  of  the  original  perception  and  action.  What 
ground  can  we  have  for  an  assumption  that  the  particular 
images,  b,  c,  and  dy  are  like  in  all  their  detail  to  any  train  of 
impressions  we  ever  have  had  ?  Admit  the  train,  what  reason 
have  you  to  affirm  that  there  is  anything  more  than  a  ge^teral 
likeness }  What  ground  have  you  for  the  assertion  that, 
if  you  could  look  into  the  past,  you  would  see  a  train  of 


302  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  XL 

impressions  B,  C,  and  D,  of  which  these  present  images  are 
copies  f  Why  must  d  be  an  "  exact  likeness  "  of  the  particular 
pleasant  eating  D  ?  These  dogmas  seem  to  me  to  be  nothing 
but  postulates.  The  fact,  so  far  as  I  observe  it,  shows  me  that, 
without  respect  for  the  past,  such  images  vary  freely  within 
a  certain  limit,  and  that  this  limit  is  fixed  by  the  universal 
connection  which  appears  in  all  of  them.  But,  if  so,  then 
what  is  associated  is  not  particular  images.  The  universal 
which  has  been  deposited  is  the  active  principle,  and  the 
particular  images  as  such  are  quite  inert. 

And  in  the  second  place  the  alleged  process  imports 
another  gross  fiction  into  the  data.  It  tells  us  that  similarity 
calls  up  an  image  b,  which  is  a  copy  of  Monday's  piece  of 
sugar.  We  have  just  seen  that,  if  present,  the  image  need 
be  no  copy  :  and  now  we  go  further.  For  in  our  elementary 
case  the  image  b  has  no  existence.  I  repeat  once  more  that 
it  is  a  pure  invention,  necessary  for  the  theory  but  absent 
from  the  fact.  When  Tuesday's  piece  of  sugar  is  present,  the 
attributes  of  whiteness  and  crystalline  appearance  reproduce 
the  ideas  of  movement  and  sweet  taste,  without  any  such  link 
as  another  and  different  piece  of  sugar.  It  is  not  merely  that 
we  can  not  find  such  an  image  now.  We  never  could  have 
found  it.  It  never  has  been  there.  And  we  need  not  ask  at 
length  if  the  Laws  of  Obliviscence  could  serve  to  obscure  it, 
unless  some  evidence  is  produced  to  show  that  it  is  more  than 
a  mere  chimsera. 

And,  as  we  have  seen,  it  is  a  chimaera  that  will  not  work. 
For  when  you  have  got  your  image  of  Monday's  sugar,  you 
are  left  precisely  where  you  were  before.  You  have  got  an 
element  which  has  just  been  born,  and  which  therefore  can 
never  have  been  contiguous  to  anything  in  its  life.  And  if 
you  say  "  But  it  resembles  what  was  contiguous ; "  then  this 
is  not  only  to  desert  your  principles,  but  it  also  tends  to 
expose  you  to  ridicule.  If  you  want  what  is  the  former  piece 
of  sugar,  you  can  not  get  it.  But  if  you  want  what  is  like  the 
former  piece,  then  you  have  it  already  iit  the  present 
perception. 

Your  fictions  do  not  help  you,  and  why  should  you  cherish 
them?     Why  invent  the  existence  of  similar  images  which 


Chap.  I.]      THE   THEORY  OF  ASSOCIATION   OF  IDEAS.  303 

lure  the  unwary  to  vicious  inferences  ?  Why  suppose  that 
"trains  of  ideas,"  of  which  the  mind  knows  nothing,  float 
across  it  in  procession,  and  then  go  on  to  manufacture  a  Law 
of  Obliviscence  which  ties  a  bandage  over  its  eyes  ?  Because, 
if  you  do  not,  you  are  forced  to  admit  that  the  mind  does  not 
go  always  from  particulars  to  particulars,  that  indeed  it  never 
can  go  from  particulars  direct  to  particulars,  that  in  short  the 
Experience  psychology  is  exploded. 

§  26.  Let  us  give  once  more  the  natural  interpretation  of 
the  simple  fact.  The  natural  view  is  that  Monday's  ex- 
perience remains  in  the  mind,  not  in  the  shape  of  particular 
images,  but  as  a  connection  between  elements  of  content. 
This  is  a  result  which  in  its  metaphysical  nature  we  can  not 
here  characterize,  but,  in  its  appearance  to  us,  it  is  easy  to 
describe.  It  is  a  tendency  to  pass  from  one  universal  to 
another,  whenever  the  first  of  these  is  presented  in  an  actual 
perception  or  image.  In  the  instance  we  are  examining,  the 
shape,  the  size,  the  person  giving,  the  where,  the  when,  and 
the  how  have  all  gone.  Nothing  is  left  but  a  tendency  to  pass 
from  element  to  element,  from  whiteness  and  crystalline  ap- 
pearance and  hardness  to  eating  and  sweetness. 

Monday's  experience,  let  us  say,  has  established  the  con- 
nection "  white-eaten-sweet."  On  Tuesday  "  white  "  is  given, 
and  so  we  have  "  this-white."  We  advance  by  means  of 
an  elementary  synthesis  to  "  this-white-eaten-sweet,"  and, 
ignoring  that  part  which  does  not  interest  us,  we  get  "this- 
eaten-sweet,"  or,  elliptically,  "  this-sweet."  I  grant  you  the 
"  sweet "  is  now  fully  particular,  but  its  particularity  has  had 
nothing  to  do  with  its  recall.  On  the  contrary  its  detail 
depends  upon  the  context  which  has  recalled  it.  And  there 
is  no  particular  image  of  "  white  "  at  all  ;  for  the  universal 
"  white  "  is  what  has  worked,  and  that  of  course  was  given  in 
the  present  perception. 

Where  is  Similarity  here  ?  It  does  not  exist.  Similarity 
implies  the  feeling  of  diversity,  and  here  the  difference  of 
particulars  never  comes  before  the  mind  ;  it  is  in  no  sense 
present. 

Let  us  give  up  Similarity  +  Contiguity  +  Obliviscence 
or  Primitive  Credulity.      Let  us   postulate  Identity  +  Con- 


304  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  IL 

tiguity,  and  then  all  is  easy.  But  there  are  two  things 
we  must  remember.  The  contiguity  is  a  connection  of  uni- 
versals,  and  is  therefore  not  the  contiguity  of  the  Association 
school.  And  the  identity  is  not  present  to  the  mind.  The 
mind,  if  you  keep  to  simple  cases,  knows  nothing  of  any 
difference.  It  goes  straight  from  what  is  given  to  an  addi- 
tional fact. 

§  27.  Let  us  state  our  view  as  a  working  hypothesis, 
something  that  need  not  be  true  or  even  possible.  Let  it  be 
granted  there  is  a  mind  X  with  certain  functions ;  let  it 
be  granted  that  X  may  be  stimulated  to  perform  again  any 
function  which  it  ever  has  performed  ;  let  it  be  granted  that 
in  every  function  there  is  a  connection  of  elements,  as  a-b  ; 
let  it  be  granted  that  presence  of  a  tends  to  excite  X  to 
perform  again  the  function  which  contains  a-d  ;  then  let  a  be 
given  in  a  fresh  context,  as  Ca.  On  this  X  is  stimulated  to 
go  on  to  b  thus,  Ca-b ;  and  the  product  Cab  now  comes 
before  the  mind — which  is  the  fact  to  be  explained.  If  this 
explanation  is  false,  admit  at  least  that  it  is  simple. 

We  are  asked  to  believe  it  is  more  in  accordance  with 
"  experience  "  to  say,  Similarity  is  a  tertium  quid  ensuing 
only  on  the  presence  of  a  pair  of  elements,  and,  when  but  one 
is  present.  Similarity  brings  the  other.  It  is  "  science  "  when 
we  asseverate  that  mental  phenomena  are  realities  which  can 
exist  only  while  they  are  perceived,  and  then  speak  of  "  re- 
calling "  them,  as  if  they  were  ambassadors  on  foreign  em- 
ployment, or  "  calling  them  up  "  as  though  they  were  servants 
in  the  kitchen,  and  as  if  "  relations  "  were  wires  that  rang  the 
bell,  or  were  fishing-lines  baited  with  similarity  to  draw  up 
from  non-existence  the  ghosts  of  the  past.  It  is  "  positive 
knowledge  "  to  make  that  come  before  the  mind  which  does 
not  come  before  the  mind,  and  then  to  remove  it  by  a 
fictitious  expedient.  Yes,  sooner  than  run  the  risk  of  believ- 
ing in  metaphysics,  there  is  no  superstition  so  gross,  no 
mythology  so  preposterous  that  we  ought  not  to  believe  in 
it,  and  believe  anything  sooner  than  cease  to  believe  in  it. 

§  28.  But  what  is  it  that  forces  us  to  these  desperate 
shifts  ?  Not  the  facts  themselves,  for  we  violate  them.  It  is 
simply  the  shrinking,  as  we  think,  from  metaphysics.      And 


Chap.  I.]       THE   THEORY  OF   ASSOCIATION   OF   IDEAS.  305 

this,  after  all,  is  nothing  but  metaphysics.  It  is  our  unreason- 
ing fidelity  to  a  metaphysical  dogma  which  has  driven  us  to 
adopt  these  embarrassing  results.  For  why  is  it  we  are  so 
sure  that  identity  is  impossible,  and  that  a  synthe&'s  of 
universals  is  a  "  survival "  of  superstitions,  which  in  the  nine- 
teenth century  are  out  of  date?  It  is  because  we  are  sure 
that  there  can  be  no  reality  but  particular  existences,  and  no 
mental  connection  but  a  relation  of  these  units ;  and  that 
hence  identity  is  not  possible.  But  this  is  of  course  a  meta- 
physical view,  and,  what  is  more,  it  is  nothing  but  a  dogma. 
The  Philosophers  of  Experience  have,  so  far  as  I  know,  never 
offered  any  proof  of  it  ;  they  have  heard  it  from  their  fathers, 
and  their  fathers  had  heard  it.  It  is  held  true  because  of 
the  continuity  of  tradition  in  a  Church,  which  must  have 
truth,  since  it  has  never  failed  to  preserve  its  continuity. 
Has  the  school  ever  tried  to  support  it  by  any  mere  rational 
considerations  .-* 

So  far  as  I  know,  it  has  been  assumed  that,  if  you  are  not 
able  to  swallow  down  this  dogma,  you  are  forced  to  accept 
an  intolerable  alternative.  You  are  given  a  choice  between 
naked  universals,  existing  as  such,  and  bare  particulars.  You 
can  not  stomach  the  first,  and  so  you  take  the  last.  But  why 
should  you  take  either }  Why  not  adopt  the  view  that  the 
real  is  the  concrete  individual,  and  that  the  bare  particular 
and  abstract  universal  are  distinctions  within  it,  which,  apart 
from  it,  are  only  two  forms  of  one  fiction  ?  You  say.  This  is 
unintelligible.  But  perhaps  you  never  heard  of  it,  or  heard 
of  it  too  late,  when  you  were  already  compromised,  and  had 
no  inclination  to  begin  life  again.  Let  it  then  be  unintel- 
ligible ;  but  permit  me  to  add  that  the  view  you  have  adopted 
calls  for  something  stronger,  to  back  it  against  facts,  than  an 
a  priori  deduction  from  a  metaphysical  alternative. 

§  29.  We  have  shown  so  far  that,  in  the  extension  of  our 
experience,  there  is  a  synthetic  construction  by  virtue  of 
identity,  and  that  association  by  similarity  has  no  part  in  it. 
We  have  shown  that  the  test  which  we  bring  to  inferences,  in 
order  to  examine  their  validity,  is  also  the  principle  which 
operates  in  all  extension  of  experience.  On  our  view  the 
origin  of  the  fact  is  explained,   and  its  existence  is  at  the 

X 


306  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  IL 

same  time  justified.  But,  on  the  fashionable  theory  of  Asso- 
ciation, early  inferences  are  made  by  what  afterwards  we  find 
to  be  the  essence  of  bad  reasoning.  And,  to  explain  the 
origin  of  this  unjustifiable  fact,  open  fictions  have  had  to  be 
invented. 

But  not  only  is  Association  by  Similarity  a  fictitious 
account  of  the  reasoning  process.  It  is  a  fiction  altogether ; 
there  is  no  evidence  for  it  at  all.  And  it  is  to  the  final  proof 
of  this  point  that  we  must  now  address  ourselves. 

Our  previous  objections  have  raised  at  least  a  presumption 
against  the  alleged  phenomenon.  Let  us  now  ask,  Is  there 
any  evidence  of  any  kind  which  tends  to  confirm  it  ?  I  know 
of  none  whatever. 

We  are  told  (J.  S.  Mill,  Hamilton,  p.  315,  note)  that  the 
elementary  case  of  the  suggestion  of  similars  will  not  come 
under  the  head  of  redintegration.  But  the  answer  to  this  is 
very  simple.  Reproduction  by  mere  similarity  is  a  fact  which, 
if  i^eal,  would  certainly  stand  by  itself  Who  doubts  it .''  But 
then  the  existence  of  this  fact  is  just  what  we  deny.  The 
general  fact  that  ideas  and  perceptions  give  rise  to  others 
which  are  like  them,  is  of  course  admitted.  But  this  not  only 
can  be  reduced  to  redintegration,  but  long  ago  it  Jias  been  so 
reduced.     I  will  exhibit  this  in  a  concrete  instance. 

§  30.  I  am  walking  on  the  shore  in  England  and  see  a 
promontory  A,  and  then  suddenly  I  have  the  idea  of  another 
promontory  B  which  is  in  Wales,  and  I  say  How  like  is  A  to 
B.  This  is  the  fact  which  is  to  be  explained.  The  false 
theory  tells  us  to  explain  the  fact  by  postulating  a  direct 
connection  between  A  and  the  idea  of  B,  for  it  says  The 
suggestion  is  perfectly  simple.  But  in  the  first  place  the 
postulate  demands  an  absurdity,  and  in  the  second  place  the 
suggestion  is  certainly  not  simple.  If  instead  of  asserting  we 
are  willing  to  analyze,  we  soon  find  the  true  explanation  of 
the  fact. 

The  content  of  A,  like  the  content  of  every  other  perception, 
is  complex,  and  has  several  elements.  Let  us  say  that  it  has 
an  element  of  form  which  is  p.  Now  let  us  look  at  B,  the 
idea  which  is  to  come  up.  That  also  possesses  a  complex 
content,  and  we  find  in  it  the  same  element/,  in  connection 


Chap.  I.]      THE   THEORY  OF  ASSOCIATION   OF  IDEAS.  307 

with  Others,  ^,  r,  j,  /.    These  are  the  conditions,  and  let  us  see 
what  follows. 

In  the  first  place  A  is  presented,  and  so  presents  /,  which 
by  redintegration  stimulates  the  mind  X  to  produce  qr. 
What  happens  then  } 

Several  things  may  happen,  and  it  is  exceedingly  difficult 
to  work  out  the  minute  psychological  conditions  which  settle 
the  result.  But  this  is  a  question  with  which  we  are  not  here 
concerned.  One  result  would  be  the  identification  of  qr 
with  A/>.  A  would  then  be  qualified  as  Apqr,  and  this 
would  be  an  unconscious  inference.  In  the  present  case  we 
are  to  suppose  that  this  can  not  happen  ;  for  we  suppose  that 
g,  r  (say  a  certain  colour  and  a  certain  size)  are  discrepant 
with  A.  What  then  may  we  expect }  We  might  expect  that 
qr  would  be  simply  dropped.  It  might  not  catch  the  attention, 
and  the  mind  might  be  arrested  by  a  new  sensation.  We 
might  expect  again  that,  if  qi'  is  not  dropped,  it  might  be  used 
as  a  means  for  a  wandering  course  through  a  train  of  ideas, 
foreign  to  both  A  and  B,  and  which  might  take  us  anywhere. 
But  we  are  to  assume  that  none  of  these  possibilities  become 
real ;  and  that  instead  the  idea  B  rises  in  the  mind.  How 
do  we  explain  this  ? 

Very  simply.  We  remember  B  had  a  content /^rj-/,  and 
now  we  have  A  which  has  brought  in  /,  and  so  introduced 
qr.  But  qr  will  not  coalesce  with  A.  Let  them  then 
instead  go  on  to  complete  the  synthesis  pqrst,  a  synthesis 
which  by  its  discrepancy  with  A  is  freed  from  union  with  it. 
But  an  independent  pqrst  is  B,  and  may  be  recognized 
as  B.  And  now,  B  being  there  along  with  A,  the  perception 
of  its  resemblance  calls  for  no  special  explanation.  This 
account  of  the  matter  appears  to  me  simple  and  natural 
and  true. 

§  31.  It  may  be  objected,  in  the  first  place,  that,  if  the 
sensation  is  simple,  this  theory  will  not  work.  I  admit  it,  and 
I  should  be  sorry  if  in  such  a  case  it  did  work.  I  would 
rather  that  any  theory,  which  I  adopt,  did  not  explain 
impossibilities.  And  that  any  actual  presentation  should  be 
simple  is  quite  impossible.  Even  if  it  had  no  internal 
characters,  yet   it   must  be  qualified  by  the  relations  of  its 

X  2 


308  THE   PRINCIPLES  OF  LOGIC.  [Bk.  IL  Pt.  II. 

environment.  And  this  complexity  would  be  quite  enough 
for  the  purpose.  For  the  identity  of  the  simple  internal 
character,  over  against  the  difference  of  two  sets  of  external 
relations,  would  give  rise  to  redintegration  and  to  the  per- 
ception of  the  resemblance.  I  think  a  sober  antagonist  will 
hardly  deny  this.  And  if  it  should  be  denied,  then  I  am 
inclined  to  reply  with  a  reductio  ad  absurdum.  If  the  sugges- 
tion is  quite  simple,  perhaps  there  is  no  difference  between 
the  similars,  or  perhaps  they  are  quite  different.  But  on 
either  alternative  they  can  not  be  similar ;  and  again,  if 
neither  alternative  is  true,  then  the  suggestion  is  now 
admitted  not  to  be  simple,  because  the  elements  have  a 
complex  content. 

I  can  think  of  another  case  where  mistake  is  possible,  and 
where  suggestion  might  seem  to  dispense  with  redintegration. 
If  an  idea  before  the  mind  is  unsteady  and  wavering,  it  tends 
to  pass  into  something  different.  This  difference  may  be 
recognized,  and  may  appear  as  an  idea,  which  is  not  the  first 
idea,  and  yet  is  seen  to  resemble  it.  But  the  unsteadiness 
will  in  no  case  be  reproduction  by  similarity.  If  the  new 
idea,  which  is  similar  to  the  other,  is  produced  by  a  change 
in  the  actual  impressions,  then  this  of  course  is  not  reproduc- 
tion at  all.  But  if  the  alteration  takes  place  apart  from  the 
stimulus  of  a  fresh  sensation,  it  will  still  be  a  case  of  redinte- 
gration. For  that  will  be  the  principle  which  determines  the 
direction  of  the  idea's  unsteadiness. 

We  must  pass  next  to  an  objection  which  I  feel  bound  to 
notice,  though  I  confess  I  am  not  able  to  understand  it.  We 
are  told  that  the  form,  say  of  a  triangle,  is  not  one  single 
feature  among  others,  which  therefore  could  call  up  the  other 
features  ;  and  that  yet  a  triangle  may  call  up  another  which 
is  similar  in  nothing  but  form  (J.  S.  Mill,  on  James  Mill,  I.  1 1 3). 
But  why  the  form  of  a  figure  is  not  to  be  a  "  feature  "  of  it  we 
are  not  told,  and  I  at  least  can  not  imagine.  I  was  glad  to  find 
when,  after  forgetting  this  passage,  I  came  on  it  again,  that 
accidentally  (§  30)  I  had  chosen  to  work  out  an  instance  where 
the  form  is  the  base  of  the  redintegration.  And  I  will  say  no 
more. 

And  there   is   another   misunderstanding  which  we   may 


Chap.  I.]     THE  THEORY  OF  ASSOCIATION  OF  IDEAS.  309 

remove  in  conclusion.  After  pointing  out  that "  in  the  very 
heart  of  Similarity  is  an  indispensable  bond  of  Contiguity  ; 
showing  that  it  is  not  possible  for  either  process  to  be 
accomplished  in  separation  from  the  other,"  Professor  Bain,  if 
I  understand  him  rightly,  goes  on  to  argue  that,  notwithstand- 
ing this,  at  least  a  partial  reproduction  by  pure  Similarity 
does  actually  take  place. 

"  It  might,  therefore,  be  supposed  that  Similarity  is,  after 
all,   but   a   mode   of    Contiguity,  namely,   the   contiguity  or 
association  of  the   different  features  or  parts  of  a  complex 
whole.     The  inference  is  too  hasty.     Because  contiguity  is  a 
part  of  the  fact   of  the  restoration  of  similars,  it  is  not  the 
entire  fact.     There  is  a  distinct  and  characteristic  step  pre- 
ceding the  play  of  this  mutual  coherence  of  the  parts  of  the 
thing  to  be  recovered.     The  striking  into  the  former  track  of 
the  agreeing  part  of  the  new  and  the  old,  is  a  mental  move- 
ment by  itself,  w^hich  the  other  follows,  but  does  not  do  away 
with.     The   effect   above  described,  as  the   consciousness   of 
agreement  or  identity,  the  flash  of  a  felt  similarity,  is  real  and 
distinct     We  are  conscious  of  it  by  itself ;  there  are  occasions 
where  we  have  it  without  the  other,  that  is  to  say,  without 
the  full  re-instatement  of  the  former  object  in  its  entireness. 
We  are  often  aware  of  an  identity  without  being  able  to  say 
what  is  the  thing  identified ;  as  when  a  portrait  gives  us  the 
impression  that  we  have  seen  the  original,  without  enabling  us 
to  say  who  the  original  is.     We  have  been  affected  by  the 
stroke  of  identity  or  similarity  ;  but  the  restoration  fails  from 
the  feebleness  of  the  contiguous  adherence  of  the  parts  of  the 
object  identified.     There  is  thus  a  genuine  effect  of  the  nature 
of  pure  similarity,  or  resemblance,  and  a  mode  of  conscious- 
ness  accompanying   that   effect ;    but   there   is  not   the   full 
energy  of  reproduction  without  a   concurring   bond  of  pure 
contiguity.     A  portrait  may  fail  to  give  us  the  consciousness 
of  having  ever  seen  the  original.     On   the  supposition  that 
we  have  seen   the  original,  this  would   be  a  failure  of  pure 
similarity"  (Bain  on  James  Mill,  I.  122-3). 

Before  I  criticize  this  passage,  let  me  show  how  easily  the 
fact  which  it  mentions  comes  under  our  theory.  When  the 
promontory  A  by  means  of  /  calls  up  q,  r,  these   are  not 


310  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  II* 

referred  to  A.  And,  unless  the  synthesis  /,  q,  r,  s^  t  is 
completed,  they  can  not  re-instate  B.  The  uneasiness  of 
partial  but  incomplete  recognition  is  caused  by  the  presence 
of  connected  elements,  such  as  /,  q,  r,  s,  which,  by  actual 
incompleteness  and  by  vague  suggestion  of  completeness,  give 
us  the  feeling  that  every  moment  another  object  is  coming. 
But,  although  the  whole  pqrs  keeps  calling  in  other  ele- 
ments such  as  ^/,  X,  y,  w,  yet  none  of  these  makes  up  a 
totality  we  are  able  to  subsume  under  any  head  which  we 
know.  Should  however  t  be  called  in,  then  B  comes  at  once. 
In  this  case  we  have  the  feeling  of  discovery,  while  in  the 
former  case  we  have  the  feeling  of  search.  And  all  is 
consistent. 

In  Professor  Bain's  account  we  have  no  consistency.  His 
view,  as  I  understand  it,  is  that  though,  for  the  full  reproduc- 
tion of  B,  contiguity  is  required,  yet  partial  reproduction  takes 
place  without  it.  In  other  words  the  stroke  of  similarity 
affects  us  enough  for  us  to  strike  into  a  former  track,  but  the 
adhesion  of  the  contiguous  bond  is  too  feeble  to  drag  on  the 
mutual  play  of  the  parts.  The  hammer  of  similarity  comes 
down,  but  the  flash  of  agreement  is  a  flash  in  the  pan,  which 
fails  to  explode  the  barrel  of  contiguity.  But  in  this  place 
again,  I  think  truth  has  been  sacrificed  to  imagination. 

If  anything  is  brought  up  which  suggests  agreement,  then 
this  must  involve  what  is  called  contiguity.  For  apart  from 
such  contiguity  there  would  be  nothing  to  recognize.  This  is 
readily  shown.  In  the  first  place  let  the  similarity  "amount 
to  identity  : "  let  the  differences,  which  went  along  with  and 
qualified  B,  be  none  of  them  called  up.  Then  what  is  there  } 
Why  nothing  but  one  part  of  the  content  of  A,  say  p.  And 
p  agrees  with  nothing  ;  for  what  can  it  agree  with  .?  There  is 
nothing  save  itself.  But  in  the  second  place,  if  the  differences 
which  qualified  B  and  made  it  B,  are  called  up,  then  obviously 
we  have  contiguity  at  once  ;  for  /  by  contiguity  has  re-instated 
pqrst.  "  Oh  but,"  I  may  hear,  "  we  do  not  go  on  to  t,  and 
so  we  never  do  get  so  far  as  B.  We  go  only  as  far  as  pqrs, 
so  that  we  are  not  able  to  recognize  the  result.  .  It  would  be 
contiguity  if  we  went  from  p  to  t :  but  if  we  stop  at  s,  it  is  not 
contiguity  at  all. 


Chap.  I.]      THE   THEORY   OF   ASSOCIATION   OF   IDEAS.  3 II 

But  this  would  surely  be  no  less  feeble  than  arbitrary.  If 
the  whole  of  the  differences  between  a  portrait  and  the  idea 
of  the  original  can  not  be  given  by  contiguity,  why  then 
should  any  of  them  }  Why  not  a/l  be  given  by  similarity  .? 
And  if  a^iy  are  given  by  contiguity,  why  should  not  a/l  be 
given,  for  all  of  them  are  demonstrably  "  contiguous  "  .?  In 
other  words  if  similarity  will  not  bring  up  all  the  differences, 
why  should  it  bring  up  any  ?  Why  should  not  all  be  left  to 
contiguity } 

Because  as  before  we  do  not  start  from  the  fact,  but  start 
from  a  vicious  theory  of  that  fact.  In  the  perception  Ap  the 
/  is  not  really  a  particular  image  ;  and  if  you  said  q,  r,  s,  t 
were  associated  with  this  mere  adjective  /,  you  would  have 
deserted  your  vicious  theory.  You  try  to  save  it  by  invent- 
ing a  fictitious  substantival  image  p,  which  then  can  be  brought 
in  by  similarity.  But  the  result  is  a  system  of  compromise 
and  oscillation.  You  will  not  boldly  say  that  A  brings  up  all 
of  B  by  similarity,  and  your  theory  forbids  you  to  say  it  does 
so  by  contiguity.  To  satisfy  both  the  fact  and  your  theory 
you  say.  One  arbitrary  part  is  done  by  one  agency,  and  the 
rest  by  the  other.  And  you  satisfy  neither  your  theory  nor 
the  fact.  For  what  is  actually  contiguous  is  not  like,  and 
what  is  supposed  like  could  never  have  been  contiguous. 
The  particular  image,  which  on  your  theory  is  called  up,  has 
never  been  contiguous  to  anything  whatever.  And  the  actual 
element,  which  does  re-instate  qrst  by  contiguity,  is  not  any- 
thing we  can  call  like  A  at  all.  It  is  an  universal  which  is 
part  of  A's  content.  Into  this  confusion  we  are  led  by  forcing 
on  the  facts  our  bad  metaphysics  ;  and  the  confusion  at  once 
gives  place  to  order  when  we  recognize  that  Association  by 
Similarity  has  no  existence. 

§  32.  We  have  seen  that  reproduction  of  a  similar  idea 
comes  under  the  general  head  of  Redintegration.  And 
if  the  English  votary  of  Association,  instead  of  declaiming 
against  the  blindness  of  Germans,  had  been  willing  to 
learn  from  them,  he  might  long  ago  have  amended  his 
theory. 

"  Si  quod  nunc  percipitur  specie  vel  gen  ere  idem  est  cnm  eo, 
quod  alias  una  cum  aliis  perceptum  fuerat,  imaginatio  etiam 


312  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  XL 

horum  perceptionem  producere  debet.  Quae  enim  specie  vel 
genere  eadem  sunt,  ea  sibi  mutuo  similia  sunt,  quatenus  ad 
eandem  speciem,  vel  ad  idem  genus  referuntur  (§  233,  234, 
Ontol.)y  consequenter  quaedam  in  iisdem  eadem  sunt  (§  195, 
Ontol.).  Quare  si  nunc  percipimus  A  specie  vel  genere  idem 
cum  B,  quod  alias  cum  C  perceperamus ;  quaedam  omnino 
percipimus,  quae  antea  simul  cum  aliis  in  B  percepimus. 
Quamobrem  cum  perceptio  ceterorum,  quae  ipsi  B  inerant  et 
in  A  minime  deprehenduntur,  vi  imaginationis  una  produci 
debeant  (§  104) ;  imaginatio  quoque  producit  perceptionem 
ipsius  B  .  .  .  . 

"  Idem  confirmatur  a  posteriori.  Ponamus  enim  nos  in 
convivio  simul  vidisse  hospites  et  vitra  vino  plena.  Quodsi 
domi  die  sequente  oculos  in  vitra  convertis,  quibus  vinum 
infundi  solet ;  extemplo  tibi  occurrit  phantasma  hospitum  ac 
vitrorum  vino  plenorum  rerumque  ceterarum  in  convivio 
praesentium.  Vitra,  quae  domi  conspicis,  specie  saltem  eadem 
sunt  cum  vitris,  quae  videras  in  convivio."  * 

Let  us  hear  now  what  Maas  has  to  say.  I  translate  from 
the  second  edition  of  his  Versuch  uber  die  Einbildungs- 
kraft,  1797. 

"  The  first  of  these  rules  we  have  mentioned  is  the  so-called 
Law  of  Similarity  :  All  ideas  which  are  like  are  associated.! 
I  am  aware  that  many  psychologists  give  this  law  a  place 
co-ordinate  with  the  law  of  partial  perception  "  [redintegration] 
"and  consider  it  independent.  But  on  this  view  the  former 
stands  too  high,  and  the  latter  too  low.  Similar  ideas  can  not 
be  associated  unless,  and  so  far  as,  either  they  or  their  marks 
form  part  of  one  total  perceptive  state.  But  this  holds  good 
without  exception.  Two  ideas,  a  and  b,  are  like  one  another 
in  so  far  as  they  have  a  common  mark  /3.  Suppose  now  that  it 
is  a  fact  that  b  has  associated  itself  with  ^."  [The  explanation 
of  this  fact  is  that]  "  b  contains  the  marks  /?,  5,  e,  and  a  the 
marks  ft  a,  7."  [On  the  presentation  of  b'\  "  the  marks  a,  7 
associate  themselves  with  the  /?,"  [which  appears  in  b,  and  ySa7 
is  then  recognized  as  ^.]     "  The  association  which  takes  place 

♦  These  quotations  are  from  §  105  of  Wolff's  Psych.  Emp,  Ed.  Nova, 
1738.     First  published  in  1732. 

t  "  Ideas  "  here  includes  perceptions. 


Chap.  I.]      THE   THEORY   OF   ASSOCIATION   OF   IDEAS. 


UNIVEIJ 


is  thus  between  connected  ideas,  which  are  parts  of  one 
perceptive  state."  s.  55.* 

I  admit  that  the  passage  is  so  brief  and  cramped  that  I  have 
been  obliged  to  interpolate  a  commentary.  But  there  are  other 
passages,  which  I  need  not  quote,  which  would  settle  the 
meaning  even  if  it  were  doubtful. 

From  these  extracts  it  will  be  plain  that  the  school  of 
Association  have  had  something  to  learn  which  they  never 
have  learnt.f 

§  33.  There  is  a  possible  objection  we  may  here  anticipate. 
"  Admitted,"  it  may  be  said,  "  that  your  theory  explains  the 
suggestion  of  similars,  yet  it  does  so  indirectly.  We  explain 
it  directly  and  by  a  simple  law.  And  the  simpler  explanation 
is  surely  the  better  one."  Anything  more  unscientific  than 
such  an  objection  I  can  hardly  conceive.  It  proposes  to  give 
a  simple  explanation  of  a  complex  case  ;  in  other  words  to 
decline  analysis,  and  to  reassert  the  fact  as  a  principle.  And 
it  proposes  in  consequence  (as  we  have  shown  at  length) 
to  treat  the  simple  as  a  complication  of  the  complex.  But  the 
price  you  pay  for  turning  a  derivative  law  into  an  ultimate 
principle  is  somewhat  ruinous.     You  have  to  import  into  the 

*  "  Die  erste  von  den  eben  erwahnten  Regeln  ist  das  sogenannte  Gesetz 
der  Aenlichkeit :  alle  ahnlichen  Vorstellungen  associiren  sich.  Es  ist 
mir  nicht  unbekannt,  dass  diese  Kegel  von  vielen  Psychologen  dem 
Gesetze  der  Partialvorstellungen  koordinirt,  und  fiir  ein,  von  diesem 
unabhangiges  Gesetz  gehalten  wird.  Allein  das  heisst  dem  erstern  einen 
zu  hohen,  dem  andern  einen  zu  niedrigen  Rang  anweisen.  Aehnliche 
Vorstellungen  konnen  sich  nur  in  sofern  associiren,  als  sie,  oder  ihre 
Merkmale,  zu  einer  Totalvorstellung  gehoren,  welches  aber  bei  ihnen  ohne 
Ausnahme  der  Fall  ist.  Zwei  Vorstellungen  a  und  b  sind  einander 
ahnlich,  sofern  beide  das  gemeinschaftliche  Merkmal  /3  haben.  Wenn 
also  b^  der  die  Merkmale  /3  8  e  zukommen,  sich  mit  a  worin  die  Merkmale 
/Say  angetroffen  werden,  vergesellschaftet ;  so  associiren  sich  a  y  mit  i3, 
sind  also  zusammengehorige  Partialvorstellungen." 

t  Sir  W.  Hamilton  not  only  refers  to  the  true  account  of  Association 
by  Similarity,  but  even  criticizes  it.  Unfortunately  he  had  not  the  least 
idea  of  its  meaning.  He  tells  us  first  that  we  are  to  discount  "  Wolff  who 
czunot properly  be  adduced."  I  have  no  notion  what  "properly"  stands 
for  here,  and  perhaps  Sir  W.  Hamilton  did  not  really  know  what  Wolff 
says.  He  then  proposes  an  emendation  in  the  passage  from  Maas, 
which  reduces  it  to  nonsense,  and  his  criticism  shows  that  he  had  no  idea 
of  the  real  meaning  of  cither  Wolff  or  his  followers  (vid.  Reidy  913-4). 


314  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  IL 

simplest  processes  a  mass  of  detail  which  is  demonstrably  not 
there.  And  this  is  surely  a  procedure  which  science  will  not 
justify. 

And  if  I  am  told,  "  At  all  events  the  process  of  suggestion, 
as  you  describe  it,  is  much  too  complex  for  a  primitive  mind," 
that  objection  once  more  only  serves  to  strengthen  me.  For  the 
process  does  not  exist  in  a  primitive  mind.  Similarity  is  a 
somewhat  late  perception,  and  hence  can  not  appear  at  an  early 
stage.  For  a  rude  understanding,  if  things  are  not  the  same, 
they  are  simply  different  To  see,  or  to  feel,  that  two  things 
are  not  the  same  and  yet  are  alike,  are  diverse  and  yet  in  part 
identical,  is  a  feat  impossible  for  a  low  intelligence.  It  demands 
an  advance  in  reflection  and  distinction  which  no  sane 
psychology  can  place  at  the  beginning  of  mental  evolution. 
No  doubt  you  may  say  that  from  the  very  first  mental  elements 
are  alike,  although  the  mind  does  not  perceive  it.  But  in 
saying  this  you  open  a  question  not  welcome  I  should  judge 
to  the  disciples  of  Experience.  For  if  states  of  mind  can  be 
alike,  and  yet  not  like  to  the  mind,  what  is  such  similarity  but 
the  identity  of  elements  within  these  states  }  The  distinction 
on  the  one  hand  between  what  is  or  was  in  the  mind,  and,  on  the 
other  hand,  that  which  is  felt  by  the  mind  or  is  now  before  ity 
is,  if  admitted,  quite  fatal  to  the  orthodox  English  creed.  We 
should  have  an  attempt  to  purchase  consistency  by  suicide. 

If  the  school  of  Association  desired  to  be  consistent,  it 
might  find  perhaps  in  the  "  mechanism  of  ideas,"  apart  from 
consciousness,  a  way  of  propping  its  tottering  beliefs.  But 
that  mechanism  implies  metaphysical  doctrines  as  to  the 
unity  of  the  soul  and  the  permanence  of  ideas,  which  in 
themselves  would  be  somewhat  difficult  to  maintain,  and 
which  would  give  the  lie  to  our  most  cherished  prejudices. 

But  if  consistency  can  be  reached  by  no  way  but  suicide, 
something  after  all  may  be  said  for  the  admission  of  the 
doctrine  we  have  adopted — that  all  association  is  between 
universals,  and  that  all  consists  in  redintegration  by  identity. 

§  34.  The  answer  no  doubt  will  be  the  old  "  Non 
possumns.  No  two  states  of  mind  can  have  anything  in 
common ;  for,  if  so,  they  would  be  the  same,  and  that  is 
impossible."    On  this  rock  of  obstinate  metaphysical  prejudice 


Chap.  L]      THE   THEORY  OF  ASSOCIATION   OF   IDEAS.  315 

our  explanations  are  broken.  It  would  be  useless  to  point  out, 
as  we  have  already  pointed  out,  to  the  disciple  of  Experience 
that  his  own  theory  has  been  wrecked  on  this  same  iron  dogma. 
He  would  say,  I  suppose,  "Let  the  facts  go  unexplained,  let 
miracles  be  invoked  and  fictions  multiplied,  let  analysis  be 
neglected  and  experience  contemned — only  do  not  ask  me  to 
be  false  to  my  principles,  do  not  ask  me  to  defile  the  grave  of 
my  fathers.  An  advanced  thinker  once,  an  advanced  thinker 
always."  And  I  could  not  answer  or  reproach.  I  respect  a 
fidelity  which  I  can  not  imitate. 

But  to  those  whose  honour  is  not  yet  pledged  I  may 
perhaps  in  conclusion  be  permitted  to  address  myself.  Do 
you  wish,  I  should  like  to  ask  in  the  first  place,  to  speculate 
on  first  principles,  or  are  you  content  to  engage  yourself  on 
special  subject  matter  }  In  the  first  case  I  would  beg  you 
seriously  to  examine  the  question  for  yourself,  and  not  to 
take  any  assertion  on  trust.  I  can  not  venture  to  anticipate 
the  result  you  will  then  reach  (if  indeed  you  reach  any),  but  I 
feel  sure  that  any  conclusion  you  do  come  to,  will  not  be  quite 
the  same  with  the  orthodox  doctrine  as  handed  down  in 
England.  And  to  those  who  are  not  prepared  for  meta- 
physical enquiry,  who  feel  no  call  towards  thankless  hours  of 
fruitless  labour,  who  do  not  care  to  risk  a  waste  of  their  lives  on 
what  the  world  for  the  most  part  regards  as  lunacy,  and  they 
themselves  but  half  believe  in — to  all  such  I  would  offer  a 
humble  suggestion.  Is  it  not  possible  to  study  the  facts  of 
psychology,  without  encumbering  oneself  with  beliefs  or 
disbeliefs  as  to  the  ultimate  nature  of  the  mind  and  its 
contents  ?  You  can  not  have  metaphysical  disbeliefs  without 
corresponding  beliefs  ;  and,  if  you  shrink  from  becoming  a 
professional  metaphysician,  these  beliefs  must  be  dogmas. 
Would  it  not  be  better  to  study  the  facts,  and  to  let  meta- 
physics altogether  alone } 

If  this  can  be  done  in  the  other  sciences,  it  surely  can  be 
done  in  psychology  too.  In  the  other  sciences  we  know  how 
it  is  done.  The  so-called  principles  which  explain  the  facts 
are  working  hypotheses,  which  are  true  because  they  work, 
and  so  far  as  they  work,  but  which  need  not  be  considered  as 
a  categorical  account  of  the  nature  of  things.     The  physicist, 


3l6  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  IL 

for  example,  is  not  obliged  to  believe  that  atoms  or  ether  do 
really  exist  in  a  shape  which  exactly  corresponds  to  his  ideas. 
If  these  ideas  give  a  rational  unity  to  the  knowledge  which 
exists,  and  lead  to  fresh  discoveries,  the  most  exacting 
demand  upon  the  most  exact  of  sciences  is  fully  satisfied. 
The  ideas  are  verified,  and  the  ideas  are  true,  for  they  hold 
good  of  the  facts  to  which  they  are  applied.  And  to  suppose 
that  the  metaphysician  should  come  in,  and  offer  to  interfere 
with  the  proceedings  of  the  physicist  or  to  criticize  his 
conclusions,  is  in  my  judgment  to  take  a  most  wrong  view  of 
metaphysics.  It  is  the  same  with  psychology.  There  is  no 
reason  why  in  this  science  we  should  not  use  doctrines  which, 
if  you  take  them  as  actual  statements  of  fact,  are  quite 
preposterous.  For  the  psychologist,  as  such,  is  not  interested 
in  knowing  if  his  principles  are  true  when  taken  categorically. 
If  they  are  useful  ways  of  explaining  phenomena,  if  they 
bring  unity  into  the  subject  and  enable  us  to  deal  with  the 
fresh  facts  which  arise,  that  is  really  all  that,  as  psychologists, 
we  can  be  concerned  with.  Our  principles  are  nothing  but 
working  hypotheses  :  we  do  not  know  and  we  do  not  care  if 
they  turn  out  to  be  fictions,  when  examined  critically. 

That  is  the  way  in  which  pyschology  surely  might  be 
studied.  And  if  we  studied  it  in  this  way  we  should  escape 
some  controversies.  I,  for  instance,  should  lose  all  right  and 
all  desire  to  criticize  the  "  Laws  of  Association  "  on  the  ground 
of  their  untruth,  if  they  only  ceased  to  proclaim  themselves 
as  statements  as  to  the  real  movement  of  the  mind.  Within 
the  same  field  of  empirical  psychology  I  should  offer  what  I 
think  is  a  more  convenient  hypothesis,  and  any  objection  to 
that  which  rested  on  metaphysics  would  be  at  once  ruled  out 
of  court.  We  might  perhaps  thus  advance  the  study  of  the 
subject  in  a  way  which  now  seems  quite  impossible.  And  if 
we  did  not  make  much  advance  in  knowledge,  we  should  save 
ourselves  at  least  a  good  deal  of  bitterness. 

§  35.  The  suggestion  is  offered  in  great  humility,  since  the 
obstacles  it  must  meet  with  are  overpowering.  The  first 
obstacle  is  the  prejudice  of  a  bad  tradition.  It  is  supposed 
that  the  psychologist  must  be  a  philosopher.  He  is  used  to 
think  himself  so,  and  he  is  not  likely  to  accept  a  lower  place. 


Chap  I.]      THE   THEORY   OF  ASSOCIATION   OF   IDEAS.  317 

And  this  objection  is  in  fact,  I  fear,  unanswerable.  I  would 
give  him  the  name  of  philosopher  for  his  asking,  but  I  could 
not  admit  him  as  a  student  of  first  principles.  And  the 
second  obstacle  is  like  the  first.  We  get  into  what,  I  suppose, 
deserves  the  name  of  an  antinomy.  The  psychologist  is  to 
confine  himself  within  certain  limits  ;  he  is  not  to  cross  over 
into  metaphysics.  But  unfortunately  if  he  is  not  a  meta- 
physician he  will  not  know  what  those  limits  are.  And  it  is 
the  same  to  some  extent  with  all  the  sciences.  The  physicist, 
for  instance,  is  constantly  tempted  to  think  that  his  ruling 
ideas  are  ultimate  facts.  And  this  temptation  is  fatal  to  the 
mere  specialist.  It  is  only,  on  the  one  hand,  a  general  culture 
and  largeness  of  mind,  or  else  some  education  in  metaphysics, 
which  saves  him  from  this  error.  And  it  is  much  worse  in 
psychology.  The  subject  brings  with  it  a  special  temptation  ; 
and,  if  all  the  truth  must  be  told,  the  same  great  minds  that 
devote  themselves  to  physics,  to  chemistry,  or  to  biology,  do 
not  take  up  psychology.  And  then  again  the  psychologist  is 
probably  a  dabbler  in  metaphysics.  A  little  metaphysics  is 
not  enough  to  show  that  his  so-called  principles  are  fictions. 
And  our  leading  English  psychologists  perhaps  only  know  a 
very  little  metaphysics.  And,  having  a  limited  acquaintance 
with  the  subject,  they  persuade  themselves,  and  (what  is 
worse)  one  persuades  the  other,  that  they  have  completely 
mastered  it.  It  is  to  be  feared  that  this  evil  must  to  some 
extent  continue. 

And  there  is  a  final  obstacle.  The  student  of  metaphysics 
may  form  an  opinion  as  to  the  real  nature  of  psychical  pheno- 
mena. And  knowing,  as  he  thinks,  the  truth  about  these 
facts,  he  will  be  led  to  insist  on  a  psychological  interpretation 
which  is  strictly  true.  He  will  interfere  with  the  empirical 
psychologist,  and  will  himself  contribute,  by  what  he  thinks 
good  metaphysics,  to  the  begetting  of  bad  metaphysics  in 
opposition.  This  is  certainly  an  error,  but  it  is  an  error,  I 
fear,  which  will  never  quite  vanish.  When  a  man  has  once 
seen  that  every  single  science  except  metaphysics  makes  use 
of  fictions,  he  is  apt  to  conclude  that  the  next  step  is  for  him 
to  remove  these  fictions  and  to  substitute  the  truth.  But,  if  he 
looked  closer,  he  would  see  that  human  beings  can  not  get  on 


3l8  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  II. 

without  mythology.  In  science,  in  pohtics,  in  art,  and  reli- 
gion it  will  always  be  found,  and  can  never  be  driven  out.  And, 
if  we  confine  our  attention  to  science,  we  must  say  that  there 
is  only  one  science  which  can  have  no  hypotheses,  and  which 
is  forbidden  to  employ  any  fiction  or  mythology,  and  that 
this  science  with  some  reason  is  suspected  of  non-existence. 

§  36.  We  have  approached  a  large  subject  which  we  can 
not  deal  with,  and  which  might  well  occasion  misgiving  and 
doubt.  We  need  give  way  to  neither  in  our  rejection  of  the 
principles  of  the  school  of  Association.  We  reject  them  in 
the  name  alike  of  metaphysics,  of  psychology,  and  of  logic. 
In  behalf  of  metaphysics  we  protest  against  the  basis  of  dog- 
matic Atomism,  and  we  protest  against  the  superstructure  of 
a  barbarous  mythology.  It  is  not  true  that  mental  pheno- 
mena are  mere  particulars.  It'  is  not  true  that  ghosts  of 
impressions  leave  their  graves.  It  is  ridiculous  to  couple  the 
existent  and  non-existent,  or  the  present  and  the  absent,  by  a 
relation  which  implies  the  presence  of  both.  In  defence  of 
psychology  we  protest  against  an  hypothesis  which  has  to 
postulate  phenomena  which  are  clearly  absent,  and  then  to 
postulate  their  removal  by  a  process  which  is  not  present. 
When  a  single  hypothesis  explains  the  facts,  it  is  surely 
unscientific  to  employ  a  complication  which  works  no  better. 
And,  in  behalf  of  logic,  we  must  protest  once  more.  The 
essence  of  inference  can  hardly  be  a  principle  which  later  we 
recognize  as  a  principle  of  error  ;  and  which,  if  the  theory  of 
Association  were  true,  we  should  hardly  get  to  perceive  was 
false.  It  is  an  ill  omen  for  Logic  if  it  fails  to  show  that  what 
in  the  highest  stage  is  accepted  as  a  canon,  was  active  from 
the  first  developement  of  the  soul  as  the  guide  of  its  conduct 
and  ruler  of  its  life. 


NOTE   TO    CHAPTER   I. 


§  I.  Though  I  have  no  space,  and  perhaps  no  strict  right,  to  deal 
with  the  subject  here,  I  must  yield  to  the  temptation  of  making  some 
very  brief  remarks  on  the  doctrines  noticed  in  §  2  of  this  chapter. 
These  go  by  the  names  of  Indissoluble  Association  and  the  Chemistry 
of  Ideas. 


Chap.  I.]      THE   THEORY   OF   ASSOCIATION   OF   IDEAS.  319 

The  first  of  these  doctrines  is  supposed  to  have  a  very  great 
metaphysical  importance.  Mere  chance  conjunction,  if  often  re- 
peated, will  beget,  we  are  told,  an  union  of  ideas  which  is  irresistible. 
This  shows  that  what  seems  to  be  a  necessary  connection  may  be 
no  more  than  an  accidental  adherence.  From  this  we  conclude 
that  a  necessaiy  connection  is  no  canon  of  truth.  And  this  proves 
that  our  trust  must  be  placed  elsewhere.  .  The  Logic  of  Experience 
tells  us,  of  course,  what  it  is  we  are  to  trust  to. 

For  myself,  in  the  first  place,  I  never  could  get  any  information 
from  that  Logic  which  seemed  intelligible,  and  so  I  will  confine 
myself  to  the  former  part  of  the  preceding  statement. 

§  2.  The  first  fault  I  have  to  find  is  that  it  does  not  go  far 
enough.  We  need  not  have  a  i^epeated  conjunction.  One  single 
instance  is  enough  to  give  rise  to  a  necessary  connection.  For,  as 
we  should  say,  what  is  once  true  is  true  always. 

§  3.  I  have  to  complain,  in  the  second  place,  that  all  kinds  of 
combination  are  called  association.  But  association  surely  implies 
that  the  elements  which  are  joined  might  not  have  been  joined. 
And  this  should  be  proved,  or  at  all  events  made  probable,  before 
co-existence  is  assumed  to  be  mere  association. 

§  4.  It  may  be  replied,  "  Even  if  the  things  are  connected,  yet, 
as  we  perceive  them,  their  union/^r  us  must  be  chance  conjunction,  and 
therefore  association."  But  this  again  should  in  no  case  be  asserted 
without  some  ground.  It  is  not  always  self-evident  that  the  mind 
could  have  had  one^  element  without  the  other.  And  where  you  fail 
to  show  that  this  is  the  case,  you  cannot  talk  of  association. 

§  5.  I  shall  be  answered,  "  What  we  prove  is  that  in  certain  cases 
mere  chance  association  has  produced  necessary  connection ;  and  we 
argue  from  this  that  it  may  be  fairly  suspected  of  doing  so  in  all. 
The  possibility  is  proved  and  the  possibility  is  enough."  I  can  not 
enter  here  into  the  merits  of  this  argument  which  I  shall  hereafter 
show  is  logically  vicious  (vid.  Bk.  III.  II.  Chap.  III.  §  22)  ;  but  suppose 
that  for  the  present  we  admit  it.  What  conclusion  follows  ?  That 
we  are  fallible  men  ?  We  knew  that  before.  That  we  are  to  trust 
to  anything  else  ?  Then  what  else  ?  Admit  for  argument's  sake  the 
possibility  that  all  our  beliefs  are  baseless,  what  then  ?  Why  nothing. 
If  we  mean  to  go  on  living  and  thinking,  we  dismiss  this  possibility 
as  idle.  Suppose  we  all  are  victimized  by  chance  conjunction,  are 
we  not  right  to  be  so  victimized  ? 

§  6.  Association  implies  other  conditions.  It  implies  contingent 
circumstances.  When  a  chance  conjunction  is  taken  by  an  error 
for  a  necessary  connection,  the  mistake  really  consists  in  defective 
analysis.     The  remedy  is  found  in  the  progress  of  analysis,  assisted 


320  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  II. 

probably  by  fresh  fact.  Where  this  remedy  is  impracticable,  no  remedy 
can  be  applied.     For  no  other  is  possible. 

§  7.  Apart  from  mental  chemistry,  which  we  shall  consider  pre- 
sently, a  connection  of  ideas  could  not  continue  to  be  necessary  when 
it  demonstrably  has  arisen  from  association.  And  this  is  quite 
obvious.  For  the  connection  of  ideas  supposes  a  content  which  is 
ideally  inseparable,  and  the  knowledge  of  the  association  involves 
this  ideal  separation.  The  experience  which  shows  the  fact  of  the 
association,  is  at  the  same  time  the  analysis  which  loosens  its  bond. 

§  8.  This  however  is  a  minor  point.  To  the  objection  that 
possibly  all  truth  may  be  nothing  but  chance  association,  we  reply  (as 
above)  that,  supposing  this  for  argument's  sake  to  be  true,  we  can 
not  trouble  ourselves  with  idle  possibilities.  But  if  you  wish  to  go 
beyond  this  idle  possibility,  you  must  show  cases  where  unreasoning 
chance  conjunction  has  produced  false  belief  without  confusion. 
You  must  show,  that  is,  that  the  belief  in  the  connection  was  wholly 
false ;  that  it  was  not  a  true  belief  in  a  real  fact  made  false  simply 
by  a  confusion  between  the  relevant  and  irrelevant  elements  in  the 
connection.     But  this,  I  think,  has  never  been  shown. 

§  9.  If  association  rests  on  conjunction  in  perception,  then  that 
is  a  valid  ground  for  belief.  It  is  deceptive  merely  so  far  as  it  is 
unanalyzed,  and  confuses  the  irrelevant  with  the  relevant.  Otherwise 
it  is  a /r^^  of  necessary  connection.  But  then  this  latter  is  not  mere 
association.  For  it  is  not  every  conjunction  in  presentation  which 
can  be  called  an  association,  but  only  those  conjunctions  which 
result  from  chance.     And  chance  disappears  before  analysis. 

§  10.  I  will  now  turn  to  the  doctrine  of  mental  chemistry. 
Elements  by  virtue  of  repeated  chance  conjunction  are  said  to 
cohere  in  such  a  way  that  they  form  a  third  product  which  has  the 
qualities  of  neither.  But  this  in  the  first  place  would  not  be 
association^  since  that  term  implies  that  the  individuals  continue.  In 
a  chemical  union  the  molecules  of  the  substances  cease  to  be  mole- 
cules of  either  substance.  It  is  therefore  nonsense  to  say  that  they 
are  associated. 

§  II.  This  of  course  may  be  said  to  be  a  question  of  words. 
But  the  fact  of  such  union  in  the  case  of  ideas  has,  at  least  in  my 
knowledge,  never  yet  been  shown.  It  can  not  be  called  impossible, 
nor  should  I  at  least  have  said  that  it  was  even  improbable,  but  I 
have  never  seen  any  certain  instance  of  it. 

§  12.  In  the  case  oi  emotions  this  "  chemical  union  "  does  seem  to 
take  place.  But  even  here  there  might  be  doubt  if  the  emotion 
should  properly  be  considered  as  an  "  union."  It  might  rather  be  a 
new  reaction  on  a  fresh  compound  material.     But,  however  that  be, 


Chap.  L]     THE   THEORY  OF  ASSOCIATION   OF  IDEAS.  321 

it  is  true  that  the  emotional  product  often  can  not  be  analyzed.  It 
can  only  be  reconstructed  perhaps  in  part  hypothetically.  And  again  if 
we  take  intellectual /w//^:^'/^;/^-,  there  is  no  doubt  that  in  the  process  of 
mental  developement  "  faculties  "  are  produced  which  are  different  in 
kind  from  what  went  before.  But  then  again  these  functions  are 
hardly  unions  of  ideas.  When  you  strictly  keep  to  mental  objects^  I 
think  you  must  say  that  no  instance  of  what  looks  hke  chemical 
combination  has  yet  been  found. 

§  13.  It  is  of  course  mere  waste  of  time  to  bring  forward  as  evi- 
dence cases  where  the  fact  of  the  association  is  not  admitted.  It  is 
for  example  a  mere  circle  to  instance  the  idea  of  visual  extension, 
since  visual  sensations  without  extension  are  the  merest  hypothesis. 
Not  only  can  this  alleged  fact  not  be  observed,  but  there  are  very 
strong  reasons  for  rejecting  it  wholly.*  It  is  not  less  idle  to  bring 
fonvard  a  product,  such  as  the  sensation  of  white,  and  then  roundly 
assert  that  it  is  the  fusion  of  different  sensations.  Perhaps  it  is,  but 
you  would  have  to  show  the  existence  of  these  sensations  in  the 
particular  case,  and  give  some  reason  for  your  belief  that  they  were 
transformed.  It  is  finally  ridiculous  to  adduce,  as  a  chemical  product, 
an  idea  which  can  be  separated  at  once  and  with  ease  into  its 
component  parts.  J.  S.  Mill  when  hard  pressed  seems  to  play  as  his 
trump  card  the  idea  of  infinity  {Ha?nilton^  Note  to  Chapter  XV.). 
But  infinity,  as  he  understands  it,  hardly  calls  for  analysis.  Of  itself 
it  falls  apart  into  its  elements,  for  it  is  a  mere  mechanical  union. 

The  conclusion  must  be  that  the  chemistry  of  ideas  is  no  more 
than  a  hypothesis.  I  do  not  think  in  any  case  it  would  be  the  right 
way  to  state  the  fact.  But  the  fact  itself  has  not  been  clearly  sho-wTi 
to  exist.  In  the  second  place,  were  we  convinced  that  mere 
chance  conjunction  was  able  to  lead  to  it,  then  nothing  would 
follow  except  what  we  know,  viz.  that  there  is  some  general 
antecedent  probability  that  any  conviction  is  false.  This  result 
makes  no  difiference  either  to  theory  or  to  practice. 

*  Vid.  Stumpf,  Raumvorstellung, 


322  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  IL 


CHAPTER  II. 

THE  ARGUMENT  FROM  PARTICULARS  TO  PARTICULARS. 

§  I.  At  the  point  which  we  have  reached  a  discussion  of 
this  subject  may  seem  inexcusable.  If  we  have  shown  that 
no  association  is  possible  except  between  universals,  and  that 
in  the  very  lowest  stages  of  mind  universals  are  used,  we  may 
fairly  be  reproached  by  the  reader  who  is  anxious  to  learn 
something  new,  if  we  linger  over  errors  the  root  of  which  has 
long  since  been  torn  up.  For  supposing  that  the  results  we 
have  attained  to  are  sound,  the  question  is  settled.  To 
reason  directly  from  particulars  to  particulars  is  wholly  im- 
possible. It  must  be  at  most  a  desire  of  the  mind  which  this 
world  can  not  gratify,  a  postulate  a  priori  given  by  an  in- 
tuition, that  disappears  before  analysis  and  is  rejected  by 
experience. 

§  2.  But  since  it  is  possible  that  the  reader  of  this  Chapter 
has  not  accepted  the  conclusions  we  obtained,  since  it  is  not 
unlikely  that  he  has  passed  them  over,  let  us  try  once  again 
if  we  can  not  do  something  to  turn  the  light  into  this  refuge 
of  darkness.  We  must  not  expect  to  persuade  the  disciple  of 
the  Experience  Philosophy.  It  is  not  for  anything  we  are 
likely  to  offer,  that  he  will  desert  the  fashionable  and  easy 
creed  in  which  he  has  been  reared.  But  at  least  we  shall 
have  tried  not  to  leave  him  an  excuse.  He  must  not  say 
that  we  have  been  afraid  to  look  his  idol  in  the  face. 

There  is  however  one  thing  we  will  not  do  for  his  sake. 
We  decline  to  supply  a  direct  examination  of  the  well-known 
chapter  in  J.  S.  Mill's  Logic.  It  would  require  much  more 
space  to  set  out  the  ambiguities  inherent  in  that  chapter,  than 
we  can  give  to  the  discussion  of  the  questioa  itself ;  a  dis- 
cussion to  which,  I  may  remind  the  reader,  I  consider  that  at 
this  stage  he  has  no  right. 


Chap.  IL]        THE  ARGUMENT   FROM   PARTICULARS.  323 

§  3.  Why  should  we  not  reason  from  mere  particulars  ? 
Do  our  reasonings  never  rest  upon  fact  ?  And  what  are  facts 
if  they  are  not  particulars  ?  Either  then  we  never,  starting 
from  fact,  conclude  to  fact,  or  else  we  infer  particulars  from 
particulars.  This  result  may  so  be  deduced  from  first 
principles.  And  common  experience  supports  the  result. 
From  cases  we  have  known  we  go  to  fresh  cases  without  an 
appeal  to  any  general  principle.  We  have  seen  something 
happen  and,  given  a  new  instance,  we  argue  at  once  that  it 
will  happen  again.  But  w^e  have  no  reason  other  than  this 
fact  to  give  for  our  conclusion.  We  thus  in  the  second  place 
have  proved  our  thesis  a  posteriori,  as  before  we  proved  it  a 
priori.  And  now  we  add  an  indirect  proof.  If  for  reasoning 
were  wanted  major  premises,  then  the  lower  animals  could 
not  reason.  But  they  do  reason,  and  therefore  the  thesis  is 
proved. 

§  4.  How  shall  w^e  escape  from  this  array  of  proofs  ?  Are 
they  not  unanswerable }  To  me  they  seem  unanswerable, 
and  I  have  not  the  smallest  wish  to  escape  them.  I  admit 
them  and  embrace  them  ;  but  I  ask  a  question,  What  is  it 
that  they  prove  ? 

They  prove  first  that,  when  we  go  from  experience  of 
facts,  this  experience  is  the  foundation  of  our  inference.  They 
prove  again  that  we  do  not  always  go  from  an  explicit  major 
premise,  and  that  therefore  another  way  of  reasoning  is 
possible.  And  in  defence  of  these  results  I  am  as  zealous  as 
any  of  my  readers  can  be.  If  he  likes  to  say  beside  that  a 
syllogism  in  extension  is  a  petitio  principii  and  no  argument  at 
all,  he  will  urge  what  long  ago  I  have  endorsed.  But  let  us 
come  to  the  conclusion.  If  you  mean  to  argue  to  no  more 
than  this,  that  experience  of  particulars  is  a  basis  of  inference, 
and  that  no  explicit  major  is  required,  I  am  ready  to  support 
you.  But  if  you  mean  to  conclude,  Therefore  we  reason  from 
particulars  as  such  direct  to  particulars,  I  object  at  once. 
The  conclusion  does  not  follow  from  the  premises,  and  it  also 
is  wholly  contrary  to  experience. 

§  5.  We  have  in  fact  to  do  here  with  a  common-place 
logical  blunder.  The  thesis  to  be  proved  is  that  an  inference 
is  made  direct  from  particulars,  as  such,  to  other  particulars. 

Y  2 


324  THE   PRINCIPLES  OF   LOGIC.  [Bk.  IL  Ft.  II. 

The  conclusion  which  is  proved  is  that  from  experience  of 
particulars  we  somehow  get  a  particular  conclusion.  Not  to 
see  the  enormous  difference  of  these  assertions  is  to  fall  into 
a  gross  ignoratio  elenchi.  To  prove  the  thesis  in  dispute  it  is 
necessary  to  assume  that  either  we  go  direct  from  particulars 
to  particulars,  or  else  advance  through  an  explicit  syllogism 
(perhaps  even  an  explicit  syllogism  in  extension).  No  sort  of 
evidence  is  offered  to  show  that  this  alternative  exhausts  the 
possibilities ;  and  it  disappears  the  moment  we  confront  it 
with  facts. 

§  6.  In  reply  to  the  assertion  that  we  are  able  to  argue 
from  particulars  to  particulars,  I  would  ask  in  the  first  place 
what  particulars  are  meant.  Am  I  to  understand  that  the 
past  experiences  in  their  particularity  are  the  premises  used 
in  this  supposed  inference  ?  If  I  am  told  this  is  so,  of  course 
I  reply  that  we  have  here  a  mere  psychological  fiction. 
Particular  images  of  past  occurrences,  which  retain  the  special 
marks  of  the  originals,  are  not  available.  The  doctrine  that 
each  perished  perception  leaves  an  unblurred  unabridged 
counterpart  of  itself,  is  a  preposterous  invention  (cf  pp.  37-9, 
and  Book  II.  II.  Chap.  I.). 

§  7.  It  is  again  a  mere  error  which  sees  in  the  lowest  form 
of  inference  the  presence  of  one  or  more  images  of  the  past, 
together  with  a  fact  which  they  are  used  to  qualify.  When  a 
present  perception  is  modified  by  the  suggestions  of  past 
experience,  these  suggestions  do  not  come  from  particular 
images  of  perished  events.  This  theory  is  a  second  pure 
invention  (cf  ibid^. 

§  8.  In  the  third  place  when,  at  a  higher  stage  of  develope- 
ment,  the  past  event  is  as  such  called  to  mind,  and  when  we 
do  argue  from  a  particular  image,  yet  even  then  we  do  not 
argue  from  its  particularity,  from  its  psychological  environ- 
ment and  temporary  colouring.  We  argue  from  the  content, 
the  idea  which  can  exist  in  different  times  and  under  diverse 
psychological  conditions.  And  once  more,  and  in  the  fourth 
place,  this  idea  itself  need  not  be  used  as  a  whole,  but  we 
may  argue  from  one  part  of  it. 

§  9.  A  child  has  come  to  know  that,  when  the  dog  is 
pleased,  he  wags  his  tail.     On  this  he  argues  that,  when  the 


Chap.  II.]        THE  ARGUMENT  FROM   PARTICULARS.  325 

cat  wags  its  tail,  it  must  be  pleased.  What  is  it  he  proceeds 
from  ?  The  error  we  are  considering  actually  supposes  that 
one  or  more  images  of  foregone  occasions,  presenting  the  dog 
pleased  and  with  his  tail  in  motion,  come  before  the  mind,  and 
that,  on  this,  the  perception  of  the  cat  now  moving  its  tail  directly 
gives  rise  to  the  conclusion.  The  cat  is  pleased.  But  the 
question  arises.  How  is  it  that  one  attribute  is  taken  from  the 
dog-images  and  given  to  the  cat,  without  the  rest  going  with 
it  ?  Does  not  this  use  of  one  part  of  the  dog-images,  and  the 
neglect  of  the  rest,  show  that  something  happens  to  the  images 
in  question,  and  that,  however  it  has  come  about,  the  in- 
ference is  not  drawn  from  the  whole  of  any  one  of  them } 
Suppose  again  that  they  differ  among  themselves,  do  we 
argue  direct  from  the  whole  of  all  of  them  1  But  if  not,  from 
what  else } 

§  10.  The  facts  I  should  have  thought  would  have  left 
little  doubt,  that  the  result  of  experience  is  a  connection  of 
attributes,  where  the  differences  of  their  particular  subjects  are 
blurred — a  confused  universal,  which  may  appear  to  the  mind 
in  a  particular,  imagery,  but  is  used  without  any  regard  to 
that.  I  confess  I  should  have  thought  that  it  was  very  clear 
that,  in  the  special  cases  where  we  argue  from  recollection,  we 
use  the  past  event  as  a  type  or  instance.  And  since  both  this 
past  event  and  the  present  perception  come  to  us  as  instances, 
we  neglect  some  of  the  differences  that  exist  between  them.  We 
do  not  know  the  principle,  but  we  feel  "  it  is  the  same  thing  " 
in  both  cases.  But,  if  so,  the  premise  from  which  the  con- 
clusion directly  comes,  is  not  the  particular.  It  is  an  universal 
extract,  what  we  call  a  "general  impression." 

§  II.  Reasoning  from  a  particular  to  a  particular  is 
obviously  an  argument  from  analogy.  In  this  we  all  know 
that  we  do  not  use  the  whole  of  that  particular  from  which  we 
argue.  It  was  an  inference  by  analogy  which  deceived  the 
child  (§  9).  He  took  from  the  dog  a  relation  of  qualities  and 
transferred  it  to  the  cat.  What  he  argued  from  was  this 
general  relation,  and  it  was  a  false  analogy,  just  because  it  was 
a  bad  generalization.  Again,  why  do  we  object  to  false 
analogies  ?  Is  it  not  because  in  them  we  treat  some  fact  as 
another  instance  of  a  rule,  when  there  is  no  common  rule  and 


326  THE  PRINCIPLES  OF  LOGIC.  [Bk.  IL  Pt.  IL 

the  facts  are  not  instances  ?     And  is  not  this  a  hint  that  in  true 
analogy  we  use  a  principle  though  we  can  not  state  it  ? 

§  12.  This  leads  us  to  put  another  question.  Suppose  that 
per  impossibile  we  did  have  before  our  minds  a  number  of 
particular  images,  and  did  argue  from  them  directly ;  would 
not  this  inference  be  a  very  bad  one  t  If  I  say  "  A,  B,  and  C  are 
a,  and  there  is  no  difference  between  D  and  A,  B,  and  C,  there- 
fore D  is  a  " — is  not  this  a  circle — a  frivolous  petitio  ?  Again 
if  I  say  "  A,  B,  and  C  are  a,  and  D  is  different  from  A,  B,  and  C, 
therefore  D  is  a  " — is  not  this  a  bad  argument,  so  glaringly  bad 
that  no  child  and  no  beast  could  be  got  to  use  it } 

But  if  we  amend  this  semblance  of  reasoning,  and  bring  it 
to  the  form  of  a  real  inference — if  we  say  "  A,  B,  and  C  are  a, 
and  therefore  D,  which  resembles  them,  is  a,"  we  are  no  longer 
arguing  from  mere  particulars.  We  are  arguing  from  the 
resemblance,  from  a  point  or  points  which  D  has  in  common 
with  A,  B,  and  C.  It  is  not  because  A,  B,  and  C  are  a,  but  it  is 
because  in  them  some  element  /3  is  a,  and  because  again  we 
find  ^  in  D,  that  we  argue  "  tlierefore  D  is  a."  For  whenever 
we  reason  from  resemblance  we  reason  from  identity,  from 
that  which  is  the  same  in  several  particulars  and  is  itself  not  a 
particular.  And  is  it  not  obvious  that,  in  arguing  from  particular 
cases,  we  leave  out  some  of  the  differences,  and  that  we  could 
not  argue  if  we  did  not  leave  them  out?  Is  it  not  then 
palpable  that,  when  the  differences  are  disregarded,  the  residue 
is  an  universal  ?  Is  it  not  once  more  clear  that,  in  vicious 
inferences  by  analogy,  the  fault  can  be  found  in  a  wrong 
generalization } 

§13.1  will  conclude  with  an  appeal  to  common  experience. 
We  all  know  very  well  that  in  our  daily  life  we  reason 
habitually  from  the  results  of  past  experience,  although  we  may 
be  wholly  unable  to  give  one  single  particular  fact  in  support 
of  our  conclusion.  We  know  again  that  there  are  persons, 
whose  memory  is  so  good  that  they  recall  past  details  in  a 
way  which  to  us  is  quite  impossible,  and  who  yet  can  not 
draw  the  conclusions  which  we  draw,  since  they  have  never 
gone  beyond  the  reproduction  of  these  details.  It  is  not  the 
collection  of  particular  facts,  it  is  the  general  impression  one 
gets  from  these   facts  which  is   really   the  sine  qua  non  of 


Chap.  IL]        THE   ARGUMENT   FROM   PARTICULARS.  327 

reasoning;  and  it  is  that   from  which  we  really  go   to   our 
result. 

If  you  begin  the  discussion  of  a  question,  such  as  this,  with  a 
vicious  disjunction,  you  can  not  go  right.  As  a  preliminary  to 
discussion  you  have  excluded  the  truth.  From  the  alternative 
— either  an  explicit  syllogism  or  an  inference  from  particulars 
to  particulars — you  can  hardly  fail  to  get  a  false  result.  You 
may  infer —  The  syllogism  in  extension  is  no  argument,  and 
thereforew^  go  from  particulars  to  particulars.  You  may  infer 
— It  is  not  possible  to  argue  from  particulars,  and  therefore  we 
reason  always  in  syllogisms,  explicit  and  (if  you  like)  also 
extensional.  But  to  me  it  is  nothing  which  conclusion  you 
adopt.  For  both  are  errors,  and  both  at  bottom  are  one  and  the 
same  ei^ror.  They  are  twin  branches  from  one  root  of  inveterate 
prejudice  and  false  assumption. 

§  14.  The  present  Chapter  has  been  so  short  that  I  take  this 
opportunity  to  deliver  my  mind  from  a  weight  that  oppresses 
it.  I  intend  to  be  guilty  of  what  some  readers  may  think 
an  unpardonable  omission.  It  is  true  that  I  do  not  undertake 
to  criticize  every  theory  from  which  I  dissent ;  but  there  is  one 
of  those  theories  which  I  propose  to  pass  over,  that  may  seem 
to  call  for  recognition  and  enquiry.  Mr.  Spencer,  in  his 
Psyclwlogy,  has  developed  a  view  of  the  nature  of  inference, 
which  despite  its  ingenuity,  despite  its  perception  of  some  of 
those  truths  which  the  syllogism  has  forgotten,  I  am  obliged  to 
consider  fundamentally  mistaken.  It  has  always  seemed  to 
me  so  arbitrary  and  so  forced,  so  far  away  in  the  end  from  the 
real  facts,  that  I  can  not  believe  a  discussion  of  it  here  would 
tend  to  throw  any  light  on  the  problems  of  logic. 

More  than  once,  I  admit,  Mr.  Spencer's  position  in  English 
philosophy  induced  me  to  think  that  I  had  no  right  to  omit  all 
notice  of  his  peculiar  views.  The  sacrifice  of  space,  the 
chance  that  I  had  failed  to  follow  the  process  which  had 
brought  him  his  results,  did  not  weigh  against  the  danger  that 
I  might  have  seemed  to  avoid  confronting  my  own  doctrines 
with  those  of  an  established  master  in  the  subject.  But  there 
came  to  my  mind  another  consideration,  which  decided  the 
result  and  fixed  my  purpose  to  omit  the  examination.     The 


328  THE   PRINCIPLES   OF  LOGIC.  [Bk.  IL  Pt.  II. 

late  Mr.  Mill  and  Professor  Bain  have  both  written  systematic 
treatises  on  logic.  They  have  entertained  a  view  of  Mr. 
Spencer's  powers  and  philosophical  performances  which  is  not 
mine.  Mr.  Mill  especially  has  expressed  his  conviction  in 
such  terms,  that  beside  it  those  praises,  I  should  otherwise  have 
felt  were  due  to  Mr.  Spencer,  would  sound  like  detraction. 
Both  must  have  been  aware  that  Mr.  Spencer  has  more 
than  once  published  what  appears  to  be  a  novel  theory  of 
reasoning.  And  yet  neither  (so  far  as  I  know)  has  ex- 
amined the  most  peculiar  and  salient  assertions  of  that 
theory. 

And  I  thought  that  I  might  venture  on  a  humble  imitation 
of  their  common  silence.  Did  they  fail  to  follow  Mr.  Spencer's 
demonstrations,  did  they  even  think  them  an  unprofitable 
subject,  in  either  case  I  claim  the  protection  of  their  authority. 
But,  if  neither  is  the  truth  and  they  considered  Mr.  Spencer 
to  be  of  one  mind  with  themselves,  and  to  say  the  same  thing 
in  a  different  form,  then  once  again  they  unite  in  excusing  me. 
I  surely  am  not  wrong  if  I  too  omit  all  criticism,  or  at  least 
delay  it  till  I  have  seen  some  cause  to  think  that  it  is  wanted. 


(    329    ) 


CHAPTER  III. 

THE  INDUCTIVE  METHODS  OF  PROOF. 

§  I.  We  have  seen  that  in  reality  there  is  no  such  thing 
as  an  inference  from  the  particular  to  a  fresh  particular.  In 
this  Chapter  we  approach  a  cognate  superstition.  In  England, 
at  least  if  we  go  with  the  fashion,  we  all  have  to  believe  in  an 
Inductive  Logic,  which,  starting  from  particular  given  facts, 
goes  on  to  prove  universal  truths.  Its  processes,  exact  as  the 
strictest  syllogism,  surrender  themselves  to  the  direction  of 
Canons,  reputed  no  less  severe  than  Barbara  and  believed 
with  reason  to  be  far  more  fertile.  I  am  afraid  I  may  lose 
the  reader's  sympathy  when  I  advise  him  to  doubt  the  union 
of  these  qualities. 

§  2.  To  question  the  existence  or  deny  the  efficacy  of 
those  methods  of  reasoning  (whatever  they  may  be),  by  which 
modern  science  has  made  its  conquests,  would  of  course  be 
absurd.  To  succeed  on  a  great  scale  is  to  prove  one's  title.  And 
it  is  not  within  the  scope  of  this  work  to  investigate  either  the 
nature  of  the  processes  which  science  employs,  or  the  amount 
of  evidence  which  it  accepts  as  proof  What  I  wish  to  assert 
is  that,  starting  from  particular  perceptions  of  sense,  there  is 
no  way  of  going  to  universal  truths  by  a  process  of  demon- 
stration perfectly  exact,  and  in  all  its  steps  theoretically 
accurate.  The  induction  of  logicians,  so  far  as  it  professes 
to  make  that  attempt,  I  shall  try  to  show  will  not  stand 
criticism. 

§  3.  We  need  not  discuss  at  any  great  length  the  Method 
which  is  called  Complete  Induction.  To  examine  a  number 
of  individuals  and  to  say  of  all  what  you  say  of  each,  is  in  the 
first  place  no  inference  to  an  universal  truth.  A  collective 
term,  if  taken  collectively,  is  no  more  universal  than  if  taken 
distributively  (p.  82)  ;  and  the  inference,  if  admitted,  does  not 


330  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  II. 

reach  the  conclusion  which  we  have  in  view.  But,  in  the 
second  place,  the  inference  itself  is  inadmissible.  In  other 
words  if  you  start  from  each  and  end  with  each,  there  is  no 
process  ;  but  if  you  predicate  of  the  collection  what  is  true 
of  each  member,  there  is  palpable  error.  The  Induction 
by  way  of  Complete  Enumeration  must  be  rejected  as  either 
tautologous  or  false  (cf  Book  II.  I.  Chap.  II.  §  5). 

Or  again  if  we  take  the  Induction  in  another  sense,  it 
changes  its  character.  If  first  by  counting  you  arrive  at  all,. 
and  then  from  y?// pass  on  to  any,  that  is  not  a  process  which 
need  be  false  or  need  merely  repeat  the  fact  it  began  with ; 
but  then  it  is  not  based  simply  upon  the  particular  data.  If 
a  flock  of  sheep  have  all  had  medicine,  I  know  that,  within  the 
given  enclosure,  any  sheep  has  been  dosed,  and  I  connect  the 
attributes  without  thinking  of  the  individuals.  The  conclusion 
is  valid  and  is  really  universal ;  but  it  implies  a  process  which 
goes  beyond  counting.  "  This  sheep  and  that  sheep  and  the 
others  are  dosed  ; "  that  is  the  first  premise  ;  but  a  second  is 
wanted.  We  may  write  it  "  This  sheep  and  that  sheep  and 
the  others  are  every  sheep  that  is  within  this  fold,"  or  again 
"  The  fold  does  not  contain  any  sheep  but  these  which  we  have 
counted."  It  is  on  the  strength  of  this  premise  that  we  go  on 
to  conclude,  "  If  any  sheep  is  now  within  the  fold  he  must  have 
been  dosed."  We  seem  to  argue  from  "  all  "  to  "  any,"  but  the 
"  all "  has  ceased  to  be  the  mere  collection. 

We  have  first  the  assurance  that  the  whole  field  has  been 
surveyed,  and  that  we  have  not  neglected  any  relevant 
matter.  Counting  is  the  way  in  which  we  attempt  to  obtain 
this  assurance.  But  the  enumeration,  if  it  is  to  be  complete, 
must  be  qualified  by  the  privative  judgment.  Nothing  in  this 
fold  can  have  been  uncounted.  The  collection  is  thus  identified 
with  every  possible  sheep  that  comes  under  the  condition  of 
being  in  the  fold.  This  is  one  side  of  our  process.  The  other 
side  consists  in  an  act  of  abstraction,  and  in  the  selective  per- 
ception of  one  connection  of  attributes  throughout  our  whole 
subject  matter.  Then,  given  an  individual  possessing  the  con- 
dition of  belonging  to  our  fold,  we  pass  at  once  to  the  other 
connected  attribute. 

Now  the  procedure  by  which  we  get  this  general  connection 


Chap.  III.]      THE   INDUCTIVE  METHODS   OF   PROOF.  33 1 

is  in  a  sense  "  inductive ; "  and  assuredly  once  more  it  has 
employed  counting.  But  then  the  counting  by  itself  is  not  the 
induction,  and  is  not  by  itself  a  generalization.  The  discrimi- 
native analysis,  which  goes  with  the  counting,  is  the  real 
agent  which  procures  the  universal,  and  which  contains  the 
"induction"  (cf.  Book  III.).  It  is  this  which  generalizes  from 
the  facts.  But  it  does  not  go  beyond  one  single  case,  since 
its  validity  depends  on  the  privative  judgment  by  which  any 
folded  sheep  must  be  one  case  with  the  sheep  observed. 

To  repeat,  if  you  confine  yourself  to  mere  counting,  you 
get  no  general  result.  If  you  attempt  to  advance  from  the 
basis  of  mere  counting  your  ground  is  unsafe.  If  you  proceed 
from  a  complete  Enumeration,  then  the  warrant  of  completeness 
falls  outside  the  counting.  What  generalizes  is  the  selective 
perception  which  isolates  and  secures  the  connection  of 
adjectives.  But  the  conclusion  depends  on  the  guarantee  of 
completeness.  It  is  valid  because  the  connection  is  found  in 
a  whole,  which  is  warranted  to  anticipate  every  possible  case 
of  a  certain  kind. 

§  4.  But  induction  by  way  of  Enumeration  is  not  the  method 
we  are  asked  to  believe  in.*  In  the  treatise  which,  partly 
from  merits  of  its  own  and  partly  also  from  other  causes,  has 
threatened  to  fasten  itself  on  us  as  a  text  book,  we  find  the 
so-called  Canons  of  Induction,  collected  and  developed  from 
other  writers,  and  formulated  with  a  show  of  rigorous  accuracy. 
It  is  the  illusory  nature  of  these  self-styled  proofs  that  I  wish 
to  point  out  in  the  present  chapter.  We  must  not  be  afraid 
of  the  shadow  of  authority.  The  balance  of  authority  among 
modern  logicians  is,  I  think,  against  the  claim  of  the  inductive 
proofs,  and  is  not  on  their  side.  And  perhaps  already,  from 
experience  we  have  had,  we  may  be  prepared  to  find  that 
Mr.  Mill  may  at  times  be  mistaken. 

§  5.  We  must  remember  above  all  things  throughout  this 
discussion  that  the  question  is  not,  Can  discoveries  be  made  by 
the  use  of  the  Methods  }  They  may  be  as  efficacious  in  actual 
practice  as  is  asserted  by  some,  or  as  practically  inadequate 

*  The  reader  of  Mill's  Logic  will  remember,  on  the  other  hand,  that 
with  him  the  whole  inductive  process  is  taken  to  stand  or  fall  with  a 
proof  by  way  of  incomplete  Enumeration. 


332  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  IL 

and  unsuited  for  work  as  is  affirmed  by  others.  That  is  not 
the  issue  which  we  have  before  us.  The  question  we  have  to 
answer  here  is,  Are  they  valid  ways  of  proof,  by  which  we  can 
go  from  facts  to  universals  ? 

For  that  is  the  claim  which  the  Canons  set  up.  "The 
business  of  Inductive  Logic  is  to  provide  rules  and  models 
(such  as  the  Syllogism  and  its  rules  are  for  ratiocination)  to 
which  if  inductive  arguments  conform,  those  arguments  are 
conclusive,  and  not  otherwise.  This  is  what  the  Four  Methods 
profess  to  be."  J.  S.  Mill,  Logic,  Bk.  III.  ix.  §  6.  "  In 
saying  that  no  discoveries  were  ever  made  by  the  four  Methods, 
he  affirms  that  none  were  ever  made  by  observation  and 
experiment ;  for  assuredly  if  any  were,  it  was  by  processes 
reducible  to  one  or  other  of  those  methods  "  (ibid.).  "  But 
induction  is  not  a  mere  mode  of  investigation."  "  Induction  is 
proof;  it  is  inferring  something  unobserved  from  something 
observed  ;  it  requires,  therefore,  an  appropriate  test  of  proof; 
and  to  provide  that  test  is  the  special  purpose  of  inductive 
logic"  (LogiCy  III.  ii.  §  5).  We  can  have  now  no  doubt  about 
the  nature  of  this  claim  ;  and  this  claim  it  is  that  we  are  going 
to  discuss. 

§  6.  I  shall  endeavour  to  show  three  things  :  first  that  the 
Four  Inductive  Methods  can  not  be  used  if  we  start  with  mere 
facts,  that  the  Canons  presuppose  universal  truths  as  the 
material  upon  which  the  work  is  to  be  done  ;  and  that  therefore, 
if  valid,  the  Methods  are  not  inductive  at  all,  in  the  sense  of 
generalizing  from  particulars.  In  the  next  place  I  shall  briefly 
exhibit  the  real  nature  of  the  reasoning  used  in  the  above  Four 
Methods,  and  shall  point  out  that  its  essence  is  not  thus  inductive. 
'And  finally  I  shall  show  that  not  one  of  the  Canons  is  a  test  of 
proof,  and  that  by  every  one  you  can  bring  out  what  is  false. 
None  of  these  three  positions  depends  on  the  others.  If  the 
Canons  are  invalid,  if  their  essence  is  not  inductive,  or  if  they 
can  not  be  applied  to  individual  facts — if  in  short  any  one  of 
these  contentions  is  established,  the  inductive  logic  is  cer- 
tainly refuted.     And  I  hope  to  establish  firmly  all  three. 

§  7.  (I.)  In  the  first  place  there  is  no  doubt  at  all  that  the 
basis,  from  which  we  are  to  start  in  induction,  consists  primarily 
of  particular  given  facts.     I  need  cite  no  passages  to  establish 


Chap.  III.]      THE  INDUCTIVE   METHODS   OF   PROOF.  333 

this  point  We  naturally  expect  then  to  see  on  the  one  side 
the  material  as  yet  untouched  by  the  Methods,  and  on  the 
other  the  operation  of  these  agents  on  the  crude  subject  matter 
with  which  they  must  begin.  This  natural  expectation  is 
doomed  to  disappointment. 

{a)  A  suspicion  of  the  shock  which  we  are  destined  to 
receive,  may  have  come  from  the  effrontery  of  the  Method 
called  "  Residues."  This  estimable  exemplar  of  "  our  great 
mental  operation  "  comes  up  to  us  placarded  as  one  of  "  the 
means  which  mankind  possess  for  exploring  the  laws  of  nature 
by  specific  observation  and  experience,"  and  then  openly  avows 
that  it  depends  entirely  on  "previous  inductions."  Unless 
supplied  beforehand,  that  is,  with  one  or  more  ready-made 
universal  propositions,  it  candidly  declines  to  work  at  all.  We 
enquire  of  "  Residues  "  where  we  are  then  to  begin,  and  she 
says,  "  I  do  not  know  ;  you  had  better  ask  '  Difference.' "  We 
anxiously  turn  to  consider  "Difference,"  and  are  staggered 
at  once  by  the  distressing  extent  of  the  family  likeness.  A 
chilling  idea  now  steals  into  the  mind  ;  but  we  have  gone  too 
far  to  retreat  at  once,  so,  resolutely  turning  our  back  upon 
"  Residues,"  we  begin  our  examination. 

{b)  We  look  at  the  samples  of  the  work  produced,  and  we 
find  the  same  thing  turning  up  everywhere.  The  material 
supplied  to  be  dealt  with  by  the  Methods  is  never  facts  but 
is  always  universals.  Sometimes  an  open  and  professed 
generalization  is  used  as  a  starting  point.  But,  where  this  is 
not  done,  the  material  is  never  a  particular  fact.  It  has  always 
been  subjected  to  such  previous  operation  that  it  is  able  at 
once  to  be  taken  and  used  as  a  "  case  "  or  "  instance."  But 
this  means  that  already  it  is  an  abstract  statement,  ideal  and 
not  real,  capable  of  repetition  with  other  environment,  and 
without  doubt  universal.  Take  the  very  first  instance  :  "  Let 
the  antecedent  A  be  the  contact  of  an  alkaline  substance  and 
an  oil.  This  combination  being  tried  under  several  varieties 
of  circumstances,  resembling  each  other  in  nothing  else,  the 
results  agree  in  the  production  of  a  greasy  and  detersive  or 
saponaceous  substance  "  {Logic,  III.  viii.  §  i).  And  this  is  the 
raw  material  which  is  supplied.  Before  I  begin  my  induction 
I   am  to  know  already  that,  under   certain   sets   of  definite 


334  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  IL 

conditions  exactly  known,  certain  results  have  followed.  But, 
if  I  know  this,  I  also  know  that  these  results  will  always  follow 
given  the  conditions.  Every  one  of  the  instances  is  already 
an  universal  proposition  ;  and  it  is  not  a  particular  fact  or 
phenomenon  at  all* 

§  8.  It  seems  at  first  a  strange  obliquity  of  instinct  to  choose 
illustrations  which  can  not  illustrate.!  But  on  turning  to  examine 
the  Canons  themselves,  our  surprise  gives  place  to  another 
feeling.  The  illustrations  have  been  selected,  not  according  to 
choice,  but  from  hard  necessity.  For  the  Canons  are  such  that 
ex  hypothesi  they  can  not  possibly  work  upon  any  material  but 
universal  propositions. 

FIRST    CANON. 

If  two  or  more  instances  of  the  phenomenon  under  investiga- 
tion have  only  one  circumstance  in  common,  the  circumstance  in 
which  alone  all  the  instances  agree,  is  the  cause  {or  effect)  of  the 
given  phenomenon. 

SECOND  CANON. 

If  an  instance  in  which  tJie  phenomenon  under  investigation 
occurs,  and  an  instance  in  which  it  does  not  occur,  have  every 
circumstance  inxommon  save  one,  that  one  occurring  only  in  the 
former ;  the  circumstance  in  which  alone  the  two  instances  differ, 
is  the  effect,  or  the  cause,  or  an  indispensable  part  of  the  cause,  of 
the  phenomeno7t. 

THIRD    CANON. 

If  two  or  more  instances  in  which  *the  phenomenori  occurs 
have  only  07te  circumstance  in  common,  while  two  or  more 
instances  in  which  it  does  not  occur  have  nothing  in  common  save 
the  absence  of  that  circumstance  ;  the  circumstance  in  which  alone 
the  two  sets  of  ijtstarices  differ,  is  the  effect,  or  the  cause,  or  an 
indispensable  part  of  the  cause,  of  the  phenomenon, 

FOURTH  CANON. 

Subduct  from  any  phenomenon  such  part  as  is  known  by 
previous  inductions  to  be  the  effect  of  certain  antecedents,  and  the 

*  Cf.  Whewell,  Philosophy  of  Discovery,  p.  263. 

t  There  is  an  exception  which  I  will  deal  with  in  §  9. 


Chap.  III.]     THE  INDUCTIVE  METHODS  OF  PROOF.  335 

residue    of   the  pJienomenoii    is   the  effect  of    the  remaining 
antecedents. 

.FIFTH   CANON. 

Whatever  phenomenon  varies  in  any  manner  wJienever 
anotJier  pJienomenon  varies  in  some  particular  manner^  is  eitJier 
a  cause  or  a?i  effect  of  that  phenomenon,  or  is  connected  with  it 
through  some  fact  of  catcsation.     (Mill,  Logic,  III.  viii.) 

Consider  the  phrases  "  only  one  circumstance  in  common,'^ 
"  every  circumstance  in  common  but  07te"  " nothing  in  common 
save  the  absence  of  that  circumstanced  Only  think  for  a 
moment  and  realize  what  they  mean,  and  then  take  on  the 
other  hand  a  given  fact  of  perception.  The  fact  is  made  a 
particular  fact  by  the  presence  of  that,  the  absence  of  which  is 
postulated  beforehand  by  these  formulas.  A  universal  judg- 
ment is  made  universal  by  just  those  attributes  which  are 
pronounced  indispensable  in  the  material  for  these  Methods. 
The  moment  you  have  reduced  your  particular  fact  to  a 
perfectly  definite  set  of  elements,  existing  in  relations  which 
are  accurately  known,  there  you  have  left  the  fact  behind  you. 
You  have  already  a  judgment  universal  in  the  same  sense  in 
which  the  result  of  your  "  induction "  is  universal.  Let  us 
take  once  again  the  very  first  instance.  The  universal  which 
you  come  to  is  "that  the  combination  of  an  oil  and  an  alkali 
causes  the  production  of  soap."  The  universals  which  you 
start  with  are  that  an  oil  and  alkali,  if  combined  under 
conditions  be  and  de,  in  each  case  produce  soap.  But  how 
can  you  deny  that  these  latter  are  universals }  No  doubt 
they  are  impure  ;  but  the  result  of  the  "  induction  "  is  surely 
not  quite  pure.  And  is  an  impure  universal  no  universal 
at  all  ?  If  you  assert  this,  you  deny  the  efficacy  of  your 
"  induction."  If  you  will  not  assert  it,  then  you  admit  that 
your  "  inductions  "  are  not  inductive,  since  the  base  they  start 
from  is  not  individual  facts.  If  we  regard  the  formulas  for  a 
little  steadily,  we  must  surely  see  that  an  "  instance  "  which 
is  capable  of  being  so  formulated,  has  had  already  done  upon 
it  that  work  which  we  heard  the  Methods,  and  the  Methods 
alone,  were  capable  of  performing.     And,  if  so,  these  Methods 


33^  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  IL 

must  retire  from  the  field  or  withdraw  their  claims.  Some- 
thing like  a  farce  has  been  played  before  us,  whether  we 
consider  the  airs  and  pretences  of  the  Canons,  or  remember 
the  promises  and  the  boasts  of  their  patron. 

§  9.  But  I  may  be  reminded  of  and  in  fairness  I  must 
quote  an  instance,  selected  by  the  author  himself,  to  show 
that  his  Methods  can  deal  with  common  material.  And  the 
instance  has  the  greater  relevancy  here,  since  he  devised  it 
expressly  to  meet  the  objection  that  the  conditions  of  his 
formulas  could  not  be  found  in  facts. 

"If  it  had  been  my  object  to  justify  the  processes  them- 
selves as  means  of  investigation,  there  would  have  been  no 
need  to  look  far  off,  or  make  use  of  recondite  or  complicated 
instances.  As  a  specimen  of  a  truth  ascertained  by  the  Method 
of  Agreement,  I  might  have  chosen  the  proposition  '  Dogs  bark.' 
This  dog,  and  that  dog,  and  the  other  dog,  answer  to  ABC, 
ADE,  AFG.  The  circumstance  of  being  a  dog,  answers  to 
A.  Barking  answers  to  a.  As  a  truth  made  known  by  the 
Method  of  Difference,  *  Fire  burns '  might  have  sufficed. 
Before  I  touch  the  fire  I  am  not  burnt ;  this  is  BC  ;  I  touch 
it,  and  am  burnt ;  this  is  ABC,  ^BC."     {Logic,  III.  ix.  6.) 

The  Canons  we  think  are  not  hard  to  content  if  this  will 
satisfy  them.  But  surely  their  author  had  forgotten  them  for 
the  moment.  By  seeing  three  barking  dogs  I  perceive  that 
they  "  have  only  one  circumstance  in  common.'*  By  standing  in 
front  of  a  burning  fireplace,  and  then  touching  the  fire  and 
being  burnt,  I  am  to  know  that  the  two  facts  "have  every 
circumstance  in  common  but  one!'  Is  not  this  preposterous  ? 
Surely  it  is  clear  in  the  first  case  that  Mr.  Mill's  way  of 
arguing  might  prove  just  as  well  that  all  dogs  have  the 
mange,  and  in  the  second  that  every  fireplace  blisters.  And 
these  conclusions  hardly  seem  to  be  sound.* 

If  we  have  succeeded  so  far  in  establishing  this  point,  then 
the    Methods    of    induction    are    placed    in    this   dilemma. 


(^ 


*  As  a  test  of  the  writer's  accuracy  in  small  points,  we  may  notice  that 
in  the  second  example  there  is  a  mistake  in  the  working  of  the  Method. 
The  right  conclusion  is  "  Touching  burns  ;  "  for  the  fire  is  not  the  differ- 
ential condition.  It  was  there  before  I  touched  it,  and  if  it  was  not  there, 
then  we  have  two  differences  and  another  kind  of  mistake. 


Chap.  III.]       THE   INDUCTIVE   METHODS   OF   PROOF.  33/ 

Because  they  presuppose  universal  truths,  therefore  they  are 
not  the  only  way  of  proving  them.  But  if  they  are  the  only 
way  of  proving  them,  then  every  universal  truth  is  unproved. 

§  10.  (11.)  The  second  assertion  I  have  now  to  make  good, 
is  that  the  process  of  the  Methods  is  not  indtictive.  I  do  not 
mean  merely  that,  as  we  have  seen,  they  can  not  be  applied 
except  to  universals.  I  mean  in  addition  that  it  is  not  at  all 
of  the  essence  of  their  process  to  bring  out  a  conclusion  more 
general  than  the  premises.  The  process  is  one  of  elimination 
(cf.  Book  III.  p.  383).  By  removing  one  part  of  an  ideal  con- 
struction you  establish  the  remainder.  And  hence  the  result 
will  be  more  abstract  than  the  whole  original  datum,  but  it 
need  not  be  more  abstract  than  some  of  the  premises  ;  on  the 
contrary  it  may  be  less  so.  If  five  plums,  two  apples,  and  ten 
nuts  balance  the  scales  against  three  pears,  two  peaches,  and 
six  grapes,  when  I  know  that  the  nuts  weigh  the  same  as  the 
grapes,  and  the  apples  as  the  peaches,  I  infer  that  the  plums 
and  the  pears  are  equal  by  an  ideal  process  of  removing  the 
rest.  But  if  this  is  "induction,"  then  ";r+  5-3=^  +  4-2, 
and  therefore  x=a!'  and  again  "A  is  either  b  or  c,  A  is  not  c, 
and  therefore  it  is  ^,"  will  also  be  inductions.  And  if  every- 
thing is  induction  which  is  not  syllogism,  then  certainly  these 
inferences  are  all  inductive.  But  such  an  assumption  would 
surely  be  quite  erroneous.  It  finds  its  parallel  in  the  counter- 
part mistake,  that,  because,  the  Inductive  Methods  are  not 
really  ^  inductive,"  therefore  they  are  syllogistic. 

The  Methods  are  all  of  them  Methods  of  Residues  or 
Methods  of  Difference,  and  they  all  go  to  their  conclusion  in 
the  self-same  way.  They  fix  a  relation  between  certain 
wholes,  and  then,  by  the  removal  of  parts  of  each,  establish 
this  relation  between  the  remaining  elements.  In  the 
Methods  of  Agreement  and  Concomitant  Variations  the 
principle  is  the  same  as  it  is  in  the  rest.  In  the  former 
the  data  are  A^C -def,  AGYi-dij]  AKL -dmn.  It  is  then 
assumed  that  the  d  in  def,  dij]  and  dmn,  can  not  be  produced 
by  a  different  cause ;  and  hence  since  BC,  GH,  KL  are 
different,  they  do  not  produce  d.  A  is  the  residue  or 
difference,  and  therefore  A  is  the  cause.  The  process  we  shall 
see  is  vicious,  but,  such  as  it  is,  it  is  elimination.     In   Con- 

Z 


338  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pr.  IL 

comitant  Variations  we  seem  to  have  A^BC  —  d^ef ;  and  then, 
when  A^  becomes  A^  we  have  A^BC  —  d^ef.  From  this 
whole  take  away  ^BC  —  ^ef,  '^BC  —  '^ef  and  the  conclusion  is 
A  —  d.  The  principle  involved  is  the  same  throughout,  and 
the  apparent  failure  to  see  this,  and  the  setting  down  of  two  or 
three  co-ordinate  axioms  for  the  different  Methods,  is  another 
sign  that  the  writer  had  never  got  really  inside  his  subject. 
The  different  Methods  are  different  applications  of  one  single 
process,  and  since  the  premises  eliminated  may  be  just  as 
abstract  as  the  conclusion  left  behind,  this  process  can  hardly 
be  called  "  inductive." 

§  II.  Having  seen  first  of  all  that  the  Canons  will  not  work 
unless  applied  to  universals  ;  having  seen,  in  the  second  place, 
that  within  these  limits  their  procedure  is  not  essentially  one 
of  generalization,  we  come  now  to  the  third  of  our  objections. 
The  Methods  are  vicious  and  the  Canons  are  false. 

(III.)  I  do  not  mean  to  say  that,  for  all  the  purposes  of 
discovery,  the  flaws  in  the  Methods  amount  to  serious 
mistakes.  Such  a  contention  would  lie  beyond  the  scope  of 
my  volume.  It  is  certain,  however,  that  independent  logicians, 
such  as  Dr.  Whewell  and  Professor  Jevons  in  our  own 
country,  and  Professors  Lotze  and  Sigwart  in  Germany,  have 
taken  a  view  of  the  process  of  scientific  discovery  which  is  not 
favourable  to  the  claims  of  the  Four  Methods.  But  whatever 
may  be  the  usefulness  of  these  Methods,  the  point  here  at 
issue  is  their  validity  as  proofs. 

What  I  wish  to  show  is  that  they  will  not  prove  anything 
beyond  this  or  that  individual  case.  They  pass  to  their  more 
general  conclusion  by  illegitimate  assumptions. 

§  12.  I  think  the  reader  will  agree  that,  if  a  method  will 
prove  a  false  conclusion  from  premises  which  are  true,  then 
that  method  must  be  logically  vicious,  and  its  Canon,  which 
serves  as  a  test,  must  be  false.  Now  it  is  stated  by  Mr.  Mill 
himself  that  the  Method  of  Agreement  will  prove  false 
conclusions  {LogiCy  Chap.  X.).  The  Method  is  "  uncertain  " 
and  has  an  "  imperfection."  But  it  still  continues  to  figure  as 
a  proof,  and  the  Canon  is  left  standing  in  its  naked  falsity. 
We  also  have  "  axioms  "  implied  in  this  Method,  which  can 
hardly  be  true  if  the  Method  is  false,  and  which  yet  are  left 


Chap.  III.]       THE   INDUCTIVE   METHODS   OF   PROOF.  339 

exposed  to  the  daylight.  We  are  told  (Chap.  X.  §  i)  that  in 
chapters  preceding  false  assumptions  have  been  made,  and 
yet  the  chapters  with  all  their  contents  are  recommended  to 
us  still  as  a  sort  of  Gospel.  And  here  I  must  frankly  confess 
myself  at  a  loss.  Can  the  writer  really  have  known  that  all  his 
Canons  were  false  statements  ?  Whether  he  did  or  did  not,  I  will 
not  here  enquire,  for  the  discussion  would  not  be  likely  to  profit 
us.  It  will  be  perhaps  convenient  for  the  sake  of  argument  to 
assume  that  he  did  not  know  the  full  vice  of  all  his  Methods. 

The  Method  of  Agreement  starts  from  the  premises  ABC 
—  def*  AGH—dij,  AKL. —  dmn:  and  its  conclusion  is  that  A 
is  the  cause  of  d.  The  principle  it  goes  on  is  (as  we  saw 
before)  that  whatever  is  different  in  the  different  cases  can  be 
eliminated.  And  this  principle  is  false,  since  a  consequence, 
such  as  d,  need  not  always  follow  from  the  same  antecedent. 
The  generalization  is  therefore  vicious,  and  the  Canon  which 
regulates  it  is  false.  The  axioms  also,  given  in  §  2  of  the 
same  eighth  chapter,  are  no  less  false.  To  make  them  true 
you  must  qualify  them  by  adding  "  in  this  one  case."  But 
that  means  you  must  destoy  their  generalizing  power. 

§  13.  The  Method  of  Difference  is  no  less  vicious.f  From 
the  premises  ABC -def,  BC  —  ef,  it  goes  to  the  conclusion 
that  A  is  the  cause  or  an  indispensable  part  of  the  cause  of 
d.  But  this  conclusion  is  fatally  unsound.  A  may  be  here  a 
single  factor  in  the  production  of  d,  the  presence  of  which  is 
quite  accidental.  The  rule  may  be  for  d  to  be  produced 
entirely  without  A,  and  for  A  to  be  present  without  pro- 
ducing d.  The  foundation  of  the  Method  i  "  that  whatever 
can  not  be  eliminated,  is  connected  with  the  phenomenon  by  a 
law  "  is  quite  false,  unless  we  add  to  it  "  m  this  one  case,^' 
and  thereby  make  it  ineffectual  for  the  purpose  of  generalizing. 

The  Method  of  Joint  Agreement  and  Difference  is  essen- 

*  I  have  of  course  altered  Mill's  lettering.     If  his  letters  mean  any- 
thing, they  involve  a  flagrant  petitioj  and  if  they  do  not,  their  suggestion 
must  tend  to  confuse  us. 
*     t  For  further  explanation  see  Book  III.  I.  Chap.  III.  §  11,  foil. 

X  There  is  no  material  difference  between  this  and  what  is  wrongly 
given,  in  the  same  §  3,  as  different,  and  as  the  ground  of  the  Method  of 
Agreement ;  for  you  have  postulated  a  connection  in  your  premises.  I 
have  given  above  the  real  ground  of  the  Method  of  Agreement. 

Z   2 


340  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  II 

tially  the  same,  and  presents  the  same  flaw.  Its  premises  con- 
sist of  ABC-^c/;  AGH-^2>;  KYA^-dmn,  BC-^/,  GYi-ij, 
KL  —  mn.  It  infers  from  these  the  conclusion  K  —  d.  The  mis- 
take is  the  same  as  that  which  vitiated  Difference.  The  right 
conclusion  is  that,  in  these  three  cases,  A  has  gone  to  produce  d. 

In  the  Method  of  Residues  the  process  is  the  same,  and  is 
bad  for  the  same  reason.  From  KBC—def,  B— /,  C  —  e,  the 
Method  goes  on  at  once  to  K  —  d.  But  it  could  do  so 
legitimately,  only  if  it  excluded  the  possibility  of  B  or  C,  or 
both,  having  influenced,  and  been  influenced  by,  A.  Other- 
wise the  conclusion  like  all  the  rest  is  vicious,  and  its  Canon 
is  false,  unless  qualified  by  the  words  "  in  this  one  case'' 

We  come  in  the  end  to  Concomitant  Variations,  and  the 
principle  of  this  has,  I  think,  not  been  formulated  with  the 
desirable  exactness.  In  the  first  place  the  words  whenever 
in  the  Canon  itself  and  invariably  in  the  Axiom  assigned  to  it 
are  both  ambiguous.  If  they  mean  that  the  groups  of  elements 
are  causally  connected,  then  this  must  rest  upon  a  previous 
Method,  and  not  upon  mere  facts.  And  in  the  second  place, 
if  we  consider  the  process  as  a  conclusion  from  these  idealized 
premises,  still  it  is  impossible  even  then  to  demonstrate  a 
result  which  will  hold  beyond  this  or  that  case  (or  cases). 
The  premises  appear  to  be  A^BC-^V/,  A^C-d'^ef,  A^BC 
—  d^ef,  and  the  conclusion  arrived  at  seems  to  be  A  —  d.  We 
have  apparently  to  eliminate  everything  but  A  —  d,  which  is 
hence  left  as  proved.  But  since  once  again  the  factors  are  not 
isolated,  we  have  the  old  mistake  of  Difference  once  more. 
The  conclusion  which  really  follows  is  "///  this  one  case  {or 
cases)  without  A  no  ^."  Because  the  modification  of  A  has 
altered  the  result,  therefore  A  is  relevant  to  d  in  this  alteration, 
or  series  of  alterations.  I  may  add  that  no  amount  of  instances 
and  of  "  approximation  "  will  suffice  to  demonstrate  logically. 

Should  however  finally  the  premises  not  have  been  so 
idealized  as  to  be  reducible  to  the  formula  we  have  given — if 
we  really  have  nothing  whatever  to  start  with  but  a  certain 
number  of  observed  concomitances — then  there  literally  is  no 
conclusion  at  all,  for  the  co-existence  always  may  be  mere 
chance  coincidence.  And,  according  as  we  understand  the 
Canon  and  the  Axiom,  we  must  pronounce  them  to  be  either 
insufficient  or  false. 


/ 


Chap.  III.]       THE   INDUCTIVE   METHODS   OF   PROOF.  34 T 

§  14.  I  have  shown  that,  if  used  in  order  to  generalize 
beyond  this  or  that  individual  instance  as  prepared  for 
treatment,  the  Methods  are  vicious,  and  their  Canons  false. 
Their  eliminative  process  will  only  show  that  the  whole 
, antecedent  has  been  concerned  in  producing  the  whole 
consequent  (cf.  Book  III).  The  attempt  to  go  further  and, 
by  isolating  the  factors,  to  transcend  the  limits  of  the  premises 
supplied,  we  have  seen  has  broken  down  at  all  poihts. 

In  the  premises  KQC-def,  BC-ef,  you  are  supposed  to 
know  that  ^^is  connected  with  ABC,  and  ^with  BC  :  what 
you  7iot  yet  know  is  if,  in  ABC,  A  is  really  a  factor.  For  it 
might  be  irrelevant,  and  BC  without  it  might  produce  def. 
But  now,  having  BC  — ^,  and  resting  on  the  assumption 
which  we  call  the  Principle  of  Identity  (Book  I.  Chap.  V.),  you 
are  sure  that,  iCBC  —  e/is  once  true,  it  will  be  true  for  ever. 
And  you  proceed  from  this  to  argue  that  BC  —  def  must  be 
false.  For  to  produce  def  B  must  have  been  altered  :  and 
since  in  ABC  — ^^  the  result  is  produced  with  no  possible 
alteration  except  mere  A,  A  there  must  be  relevant  to  the 
presence  oidef.  Hence  A  in  this  case  (of  ABC  — def)  must 
be,  directly  or  indirectly,  relevant  to  d.  But  you  must  not  go 
further,  and  try  in  any  way  to  specify  the  connection.  For 
you  can  not  do  that  without  closing  possibilities,  and  assum- 
ing something  not  given  in  your  premises.* 

And  we  must  not  forget  that  even  this  conclusion  depends 
on  our  having  assumed  in  the  premises  that,  in  ABC  — def,  d 
is  not  irrelevant.  Unless  we  are  perfectly  sure  beforehand 
that  the  whole  def  has  been  produced  by  ABC,  we  can  not 
advance  one  single  step.  This  shows  once  more  how  absurd 
it  is  to  imagine  that  the  Methods  can  be  applied  to  particular 
facts.  They  depend  entirely  on  such  an  artificial  preparation 
of  the  material  supplied,  as  has  already  reduced  it  to  the 
form  of  an  universal.  It  would  be  waste  of  time  to  dwell 
further  on  the  detail  of  the  Four  (or  Five)  Methods,  since  the 
process  in  all  is  the  same  at  bottom.f 

*  I  should  like  here,  and  on  the  whole  subject,  to  refer  to  Lotze's 
Logik,  II.  VII. 

t  I  must  refer  to  the  following  Book  for  an  account  of  inference  by 
way  of  Elimination. 


342  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  XL 

§  15.  We  have  seen  that  the  Methods  are  not  "inductive," 
since  they  will  not  generalize  beyond  the  given  instance. 
They  fail  again  of  being  "inductive,"  since  they  can  not  be 
applied  to  simple  facts.  They  will  not  work  unless  they  are 
supplied  with  universals.  They  presuppose  in  short  as  their 
own  condition  the  result  they  profess  alone  to  produce.  Once 
more,  the  essence  of  their  procedure  is  as  much  deductive  as 
it  is  "inductive."  The  conclusion  in  some  cases  has  less 
generality  than  some  of  the  premises. 

On  any  one  of  these  grounds  (and  I  hope  on  all  of  them) 
we  may  set  down  the  Inductive  Logic  as  2,  fiasco.  And,  if  I 
am  told  that  these  flaws,  or  most  of  them,  are  already 
admitted  by  Inductive  Logicians,  I  will  not  retract  the  word 
I  have  used.  But  to  satisfy  the  objector  I  will  give  way  so 
far  as  to  write  ior  fiasco,  confessed  fiasco. 

§  16.  If  it  really  is  the  case  that  the  Methods  are  not 
sound ;  if  it  really  is  the  case  that  the  Canons  are  not  true ; 
if  it  really  is  the  case  that  "induction"  is  not  proof,  and 
that  he  has  all  along  known  this,  and  been  well  aware  of 
it — in  that  case  I  would  suggest  to  the  Inductive  Logician 
that  he  has  provoked  a  possible  harsh  remark.  And  however 
mistaken  that  harsh  judgment  might  be,  yet  I  can  not  help 
thinking  that  it  would  be  better  if  he  were  to  tell  the  public, 
what  they  certainly  do  not  know,  and  the  opposite  of  which 
his  too  large  professions  have  led  them  to  believe.  But  if,  as 
I  suppose,  the  Inductive  Logician  himself  makes  the  mistake 
which  his  public  has  accepted — if,  that  is,  while  admitting 
that,  like  all  things  human,  his  Methods  have  "  imperfections," 
he  has  no  idea  that,  taken  as  proofs,  they  are  radically 
vicious — in  that  case  I  will  end  by  expressing  the  hope  of  a 
final  agreement.  By  abridging  claims  that  will  not  stand 
criticism,  and  by  reforming  the  root  and  principle  of  his  fabric, 
he  will  bring  no  ruin  to  the  bulk  of  his  edifice.  Even  if  we 
confined  ourselves  to  Mr.  Mill's  Logic,  we  should  find  that, 
when  his  so-called  Four  Inductive  Methods  were  wholly 
removed,  and  his  inference  from  mere  particulars  banished  as 
a  misunderstanding,  the  more  valuable  and  even  the  larger 
part  of  his  discussions  on  Science  would  remain  untouched. 


(     343     } 


CHAPTER  IV. 

JEVONS'   EQUATIONAL   LOGIC 

§  I.  It  is  pleasant,  after  leaving  the  delusions  of  one's 
youth,  to  find  oneself  in  contact  with  something  like  fact.  The 
Equational  Logic  has  proved  by  its  results  that  it  has  a  hold 
on  the  world  of  reality.  What  works  must  at  least  be  partially 
right.  And  this  new  theory  of  logic  does  work.  One  may 
see  that  its  method  remains  inapplicable  to  part  of  its  subject. 
One  may  question  its  convenience  in  certain  cases,  and  even 
doubt  its  formula  in  all.  But  one  must  believe  so  much  as 
this.  At  the  lowest  estimate  the  new  system  will  prove  what- 
ever the  syllogism  is  able  to  prove.  In  some  points  it 
certainly  is  a  far  more  rigid  test  of  true  reasoning.  It  deals 
very  easily  with  many  of  those  problems  which  accommodate 
themselves  to  numerical  reasoning.  And  it  maintains,  on  the 
ground  both  of  reason  and  experience,  that,  in  comparison 
with  the  syllogism,  it  is  both  easier  to  learn  and  harder  to 
forget. 

In  writing  this  chapter  on  equational  logic,  as  it  appears 
in  the  theory  of  Professor  Jevons,  I  wish  I  could  do  two 
things  I  can  not  do.  I  wish  I  could  give  an  account  of  the 
doctrine  intelligible  to  those  who  have  no  acquaintance  with 
it.  And  I  wish  I  could  form  something  like  an  estimate  of 
its  educational  value  and  practical  powers.  But  both  want  of 
space  and  want  of  experience  compel  me  to  a  narrower  and 
less  grateful  task.  The  object  of  this  chapter  is  to  ask  if  that 
account  of  the  reasoning  process  which  has  been  offered  us  is 
strictly  accurate,  whether  as  a  theory  it  is  free  from  mistakes. 
An  answer  in  the  negative  will  be  given  to  this  question. 

§  2.  We  may  divide  the  enquiry  into  three  main  parts.  In 
the  first  (A)  we  shall  ask  if  propositions  are  identities  :  in  the 
second  (B)  if  direct  reasoning  consists  in  substitution.     In  the 


344  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  II. 

third  (C)  we  shall  discuss  the  Indirect  Method,  and  with  it 
the  claims  of  the  Logical  Machine.  It  may  prove  convenient 
to  state  beforehand  the  main  results  which  we  expect  to  reach. 
We  shall  show  in  the  first  place  (A)  that,  though  every  pro- 
position does  and  must  assert  identity,  yet  that  is  not  the 
object  of  all  propositions.  Our  second  conclusion  (B)  will  be 
that  substitution  is  not  the  real  essence  of  reasoning,  and  that 
certain  inferences  will  not  by  fair  means  come  under  this  head. 
We  shall  show  again  that,  although  most  arguments  can  be 
exhibited  in  the  form  of  equations,  yet  the  formula  of  inference 
which  our  author  has  given  is  not  correct.  In  the  third  place 
(C)  we  shall  argue  that  the  Indirect  Method,  though  perfectly 
valid,  does  not  proceed  by  substitution  :  and  finally  we  shall 
give  our  reasons  for  contesting  a  part  of  the  claims  put  forth 
by  the  Machine.  The  reader  is  supposed  to  have  made  some 
acquaintance  with  the  early  part  of  The  Principles  of  Science. 

§  3.  (A)  In  asking  if  propositions  are  equations,  we  must 
remember  that  the  sign  of  =  does  not  mean  equal  (cf  snp. 
p.  24).  It  denotes  sameness  or  identity.  So  that  the  word 
"  equation,"  which  we  have  chosen  to  start  with,  may  at  once 
be  dismissed.  The  question  is.  Do  judgments  consist  in  the 
assertion  of  identity  ?  This  point  has  already  come  before  us, 
and  great  part  of  what  follows  is  repetition. 

1.  If  we  dismiss  all  theories  and  look  simply  at  the  facts, 
then  to  ask  that  question  is  to  answer  it  in  the  negative.  How 
can  it  be  said  that  in  "  Caesar  is  sick,"  or  "  This  pond  is  frozen," 
or  "  Mammals  are  warm-blooded,"  we  really  mean  to  assert 
self-sameness?  To  say  that,  in  making  such  statements  as 
these,  our  real  object  is  the  denial  of  difference — that  we  wish 
to  say,  Although  Caesar  is  sick  he  still  is  Caesar — is  palpably 
absurd.  We  do  not  wish,  premising  the  difference,  to  insist 
on  the  identity.  The  difference  itself  is  the  information  which 
we  wish  to  convey. 

2.  If  all  propositions  asserted  mere  identity,  then  every 
proposition  would  have  to  be  false.  If  A  =  B  and  B  =  BC, 
and  we  go  from  this  to  the  conclusion  A  =  C,  then  either  B 
makes  a  difference  to  A  or  it  makes  no  difference.  In  the  one 
case  the  proposition  becomes  quite  false,  and  in  the  other  it 
disappears,  since  B  =  o.     How  can  it  be  true  that  ABC  is 


C.iiAP.  IV.]  JEVONS'    EQUATIONAL   LOGIC.  345 

the  same  as  A?     Is  BC  nothing,  then   nothing  is  asserted. 
Is  BC  a  difference,  then  how  are  they  the  same  ? 

Partial  identities  are  thus  all  false  ;  but  simple  identities 
will  fare  no  better.  If  "  =  "  is  taken  to  stand  for ''  is  the  same 
as,"  then  "A  =  B"  can  not  possibly  be  true.  If  there  is  no 
difference,  then  nothing  is  said  :  if  anything  is  said,  then  same- 
ness is  denied. 

3.  It  is  obvious,  if  we  are  to  keep  to  identity,  that  sub- 
ject and  predicate  must  be  wholly  the  same.  AB  =  AB, 
ABC  =  ABC.  But  even  here  it  is  doubtful  if  we  can  stay. 
For  even  when  we  reach  a  tautologous  statement  we  have  still 
a  difference  in  the  position  of  the  terms  (cf  Book  I.  Chap.  V.). 
If  we  wish  to  be  consistent  even  that  must  go.  We  must 
take  one  side  of  our  former  reduplication  ;  we  must  say,  for 
instance,  AB  or  ABC.  In  that,  having  given  up  our  search 
for  identity,  we  suddenly  find  the  whole  content  of  our 
assertion.  Assume  AB,  then  A  is  B.  Assume  ABC,  then 
A  is  C.  In  our  seeking  to  get  an  equational  truth,  we  got  all 
the  differences  together  on  each  side.  But  the  synthesis  of 
these  differents  was  just  what  we  really  wanted  to  assert. 
Strike  out  one  side,  and  strike  out  the  "  =,"  and  we  have  the 
content  of  the  whole  judgment* 

Assertion  is  not  confined  to  the  affirmation  of  sameness, 
and  identity  and  equality  are  but  one  kind  of  predicate.  If 
we  use  the  language  of  the  traditional  logic,  then  in  "  S  =  P  " 
the  "  =  "  has  nothing  to  do  with  the  copulS. :  it  falls  entirely 
within  the  predicate,  and  "A  =  AB"  is  "A  -  =  AB."  If 
we  wish  to  say  that  A  is  equal  to  or  the  same  as  B,  the  natural 
mode  is,  I  think,  to  say  that  A  and  B  are  the  same  or  equal. 
If  we  will  not  do  that,  and  so  openly  admit  the  existence  of 
difference,  we  must  come  in  the  end  to  "  A  =  B,"  on  the  left 
hand  side,  is  just  the  same  as  "A  =  B,"  on  the  right  hand 
side.     And  since  the  sides  are  different  even  that  is  not  true. 

§  4.  The  foregoing  section  merely  asserts  that  a  difference 
is  affirmed  by  every  proposition.  Judgment  can  not  be  reduced 
to  one-sided  identification.  In  the  attempt  to  reduce  it  we 
found  that  we  got  the  whole  matter  of  the  judgment  on  each 
side  of  the  copula.  Thus  in  "  sodium  =  sodium  metal  con- 
*  We  are  not  dealing  here  with  "  simple  identities."     For  them  see  §  6. 


34^  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Pt.  II. 

ducting  electricity  "  the  judgment  falls  on  the  right  hand  side. 
The  assertion  consists  in  the  synthesis  with  sodium  of  the 
being  a  metal  and  conducting  electricity ;  and  when  we  know 
that,  the  "sodium  "  and  the  "  =,"  of  the  subject  and  copula, 
are  false  or  meaningless.  You  say  that  it  makes  no  difference 
to  sodium  that  it  is  a  metal  and  conducts  electricity.  That 
surely  is  a  rather  odd  method  of  saying  that  there  is  no 
difference  whatever  to  make,  and  a  still  more  eccentric  method 
of  implying  that  this  makes  all  the  difference  to  sodium. 

(  §  5.  No  proposition  asserts  mere  identity,  but  without  the 
statement  or  implication  of  identity  no  judgment  can  be  made. 
The  solution  of  this  puzzle,  which  the  end  of  the  foregoing 
section  hints  at,  is  that  sameness  and  difference  imply  one 
another,  and  are  different  sides  of  the  self-same  fact.  Mere 
identity  or  difference  is  therefore  unmeaning.  And  hence, 
although  it  is  false  that  in  judging  we  always  mean  to  identify 
the  subject  and  predicate,  yet  in  every  judgment  an  identity 
can  be  found.  J  For  where  sameness  is  asserted  difference  is 
presupposed.  Where  difference  is  asserted  there  is  a  basis  of 
sameness  which  underlies  it.  And  it  follows  as  a  consequence 
that,  if  you  do  not  mind  your  implications  being  put  on  a  level 
with  your  meanings,  you  can  show  every  judgment  in  the  form 
of  differences  united  by  identity.  - 

§  6.  For  in  every  judgment  the  differences  joined  may  be 
taken  as  the  qualities  of  a  single  subject  (cf  sup.  p.  29,  and 
p.  168).  In  "  sodium  =  sodium  metal "  we  assert  that  within  the 
subject  called  sodium  the  attributes  sodium  and  metal  are  con- 
joined ;  and  if  you  please  you  may  express  this  by  saying,  that, 
under  the  differences  sodium  and  metal,  there  is  yet  no  change 
from  one  subject  to  another.  Again,  in  "  Equilateral  triangle  = 
equiangular  triangle  "  what  I  mean  to  say  is  that,  despite  these 
differences,  you  still  have  one  and  the  same  triangle,  or  again 
that,  if  one  of  these  qualities  exists,  you  will  have  the  other 
in  the  self-same  subject.  Take  again  "The  Pole  Star  =  the 
slowest-moving  star : "  this  means  either  that  one  star 
possesses  these  two  differences,  or  that,  in  spite  of  these 
differences,  the  star  is  the  same.  In  every  case  we  have 
identity  and  diversity,  and,  though  we  accentuate  one  or  the 
other,  yet  in  every  case  both  must  co-exist. 


Chap.  IV.]  JEVONS'   EQUATION AL   LOGIC.  347 

I  will  illustrate  the  foregoing  by  other  instances.  Take 
"These  fifteen  statements  are  every  one  perjuries."  The 
identical  subject  is  here  either  each  statement  or  the  quality 
of  perjury  which  appears  in  each.  There  are  hence  four 
meanings.  In  the  first  I  assert  that  in  every  statement 
perjury  must  be  added  to  its  other  qualities.  In  the  second 
I  deny  that,  though .  the  statements  are  false,  we  have  any 
right  to  abolish  the  perjury  by  making  thirty  statements  out 
of  fifteen.  In  the  third  I  complain  that  a  single  crime  has 
occurred  with  fifteen  different  sets  of  details.  In  the  fourth  I 
refuse  to  admit  the  diversity  of  the  fifteen  qualifications  as  any 
proof  that  the  crime  is  not  the  same. 

Or  take  the  instance  of  equality  or  sameness  itself.  When 
I  say  that  A  and  B  are  equal,  I  assert  that  in  the  differents  A 
and  B  their  quantity  x  is  for  all  that  the  same.  If  I  say  "  A 
and  B  are  precisely  the  same,"  I  must  first  take  A  and  B  as 
differenced  by  place  or  time  or  some  other  particular,  and  then 
against  that  assert  their  identity.  The  equality  in  one  case 
and  the  sameness  in  the  other  may  be  treated  as  the  subject 
in  which  A  and  B  co-exist  as  attributes. 

If  the  doctrine  already  put  forward  is  true,  there  can  be  no 
such  things  as  "simple  identities."  "  Equiangular  triangle  = 
equilateral  triangle "  is  false  if  it  denies  the  difference  of 
quality,  or  is  false  if  it  ignores  the  distinction  of  subjects.  The 
identity  it  asserts  must  exist  under  differences.  Thus  among 
triangles  the  subject  of  equilateral  is  one  and  the  same  with 
the  subject  of  equiangular.  The  natural  way  to  state  the  fact 
is  to  say,  The  different  subjects  are  the  same,  or  The  diverse 
qualities  imply  one  another. 

§  7.  The  result  of  our  enquiry  as  to  propositions  is  not  of 
good  augury  for  the  doctrine  of  Substitution.  True  we  find 
that  all  subjects  assert  an  identity,  but  then  they  no  less  assert 
a  difference.  Our  sign  "  =  "  has  turned  out  quite  inapplicable. 
If  S  and  P  are  made  quite  identical,  the  judgment  disappears 
or  falls  only  on  one  side.  If  again  S  and  P  are  allowed  to  be 
different,  the  sign  of  identity  asserts  a  falsehood.  This  so  far 
is  ominous.  It  is  ominous  again  that  every  identity  can  be 
shown  as  the  connection  of  attributes  within  a  subject.  And 
there  is  another  omen  we  have  not  yet  noticed.     All  judg- 


34^  THE   PRINCIPLES   OF   LOGIC.  [Bk.  II.  Pt.  IL 

ments,  we  long  ago  have  found,  can  be  understood  as  assertions 
of  identity.  But  the  class  of  relations  in  time  and  space,  it 
appears,  are  not  amenable  to  the  Method  of  Substitution,  or  at 
least  in  public  decline  to  appear  so  (cf.  Book  I.  p.  24).  I  can 
not  but  think  that  with  such  auspices  against  it  any  cause 
must  be  lost. 

§  8.  (B)  We  come  now  to  the  second  branch  of  our 
subject.  Does  the  process  of  reason  consist  in  substitution  ? 
The  foregoing  has  shown  that  this  is  not  possible. 

(i)  The  terms  which  we  substitute  must  be  the  same  :  but 
if  the  same  then  you  can  not  substitute.  If  your  process  does 
not  give  you  a  difference,  it  is  no  process.  If  it  gives  you  a 
difference  you  have  broken  the  identity.  Thus  if  reasoning 
consists  in  substitution,  its  essence  lies  in  the  substitution  of 
differ ents. 

Let  us  take  as  an  example,  "  A  is  equal  to  B,  and  B  to  C, 
and  therefore  A  to  C."  It  is  impossible  here  by  substitution 
of  idtinticals  to  come  to  any  conclusion  whatever.  For  what 
is  there  identical  ?  A  is  not  the  same  as  B,  nor  B  as  C,  nor  is 
"  equal  to  B  "  the  same  as  A.  The  identity  really  lies  in  the 
quantity  of  A,  B,  and  C.  The  quantity  of  A  and  B  is  the 
same,  and  so  is  that  of  C  and  B.  The  quantity  therefore  of 
A  and  C  is  the  same.  But  you  can  not  show  this  by  substi- 
tution. For  in  the  quantity  of  each  there  is  no  differe7ice.  The 
terms  are  x  K,  x^,  x  Q.  Now  if  you  substitute  ;i:  A  for  ;ir  B, 
you  substitute  things  which  are  not  the  same.  But  if  you 
substitute  mere  x,  you  do  nothing  at  all,  for  already  you  have 
the  term  x^.  A  is  equal  to  B,  but  it  is  not  the  same.  The 
quantity  is  the  same,  but  it  is  one  and  not  two. 

The  real  process  of  the  reasoning  consists  in  connecting 
the  differences  A  and  C  on  the  basis  of  their  common  identity 
X.  It  may  also  be  stated  as  a  substitution.  Take  x  with 
any  one  of  the  differences,  and  substitute  x  with  any  other 
difference.  The  differences  then  found  co-existing  in  x  will  be 
the  conclusion  which  we  require.  But  this  substitution  is  a 
replacement  by  differents. 

§  9.  (2)  Substitution,  so  far  as  it  works  at  all,  is  an  in- 
direct method  of  synthesizing  differences.  The  rule  is  to 
substitute   the   "expression"   for   the   term.      But    the    "ex- 


Chap.  TV.]  JEVONS    EQUATIONAL   LOGIC.  349  . 

pression "  is  the  judgment  about  the  term.  The  rule  then 
says  "  Substitute  the  judgment  for  the  term."  In  other  words, 
a  term  will  not  do  ;  you  must  have  a  premise,  and  that  means 
a  judgment  You  must  leave  your  identity  and  get  to 
differences. 

In  "  sodium  is  metal  and  conducts  electricity "  (§  4), 
sodium-metal  takes  the  place  of  sodium,  and  metal  gives  way 
to  metal-conductor,  and  we  say  this  makes  no  difference  to 
sodium,  or  sodium  is  the  same  with  all  this  difference.  But 
the  real  subject,  which  remains  the  same,  is  something  which 
underlies  these  differences  ;  and  the  real  process  is  the 
addition  of  difference  which  developes  the  connection  of 
attributes  in  this  subject.  It  is  entirely  to  mistake  our  object 
in  view  if,  while  we  try  to  get  the  synthesis  of  diverse  attri- 
butes, we  talk  as  if  all  we  wanted  was  to  keep  the  identity  of 
the  subject.  It  is  simply  to  stand  the  process  on  its  head,  if 
we  make  every  step  by  uniting  differences,  and  then  speak  as  if 
throughout  we  had  done  nothing  but  remove  them. 

"  Substitute  for  the  terms  their  expressions,"  that  is  in 
other  words  comdme  the  premises.  It  is  an  artificial  way  of 
performing  the  old  task.  For  reasons  which  I  can  not  here 
enter  into,  the  artifice  in  some  cases  is  very  useful.  But  it  is 
simply  the  syllogism  turned  upside  down,  and  it  is  confined 
to  the  same  insufficient  limits. 

§  10.  (3)  The  method  of  Substitution  has  set  itself  free 
from  some  of  the  superstitions  of  the  traditional  logic.  For 
certain  purposes  it  is  far  more  useful.  Everything  again  that 
can  be  proved  by  syllogism  can  also  be  proved  by  its  modern 
rival.  But  on  the  other  hand  Substitution  will  prove  nothing 
that  can  not  be  shown  by  syllogism.  The  limit  of  both  is 
precisely  the  same.  They  are  confined  to  the  relation  of 
subject  and  attribute  and  the  connection  of  attributes  within  a 
subject ;  and  beyond  that  category  neither  will  work  (cf. 
Part  I.  Chap.  11.  §  6). 

^To  prove  syllogistically  that,  because  A  and  C  are  both     ]  , 
equal  to   B,  they  are  equal  to  one  another,  is  quite  impos-        ^ 
sible.*  ^But  it  is  just  as  impossible  to  prove  the  conclusion  by    / 

*  "  Quantity  of  A  is  the  same  as  quantity  of  B,  quantity  of  B  is  the 
same  as  quantity  of  C,  and  therefore  quantity  of  A  is  quantity  of  C  "  will 


350  THE   PRINCIPLES   OF   LOGIC.  [Bk.  XL  Ft.  II. 

substitution.  The  premises  you  have  got  are  A  =  A  equal  to 
B,  B  =  B  equal  to  C  ;  and  the  qiiaterfiio  terminorum  can  only 
be  avoided  by  taking  the  premises  in  a  sense  which  is  false. 

It  is  needless  to  repeat  against  the  equational  logic  the 
objections  we  have  urged  against  the  syllogism.  If  a  logic 
will  not  deal  with  the  syntheses  of  degree,  of  space,  and  of 
time ;  if  even,  as  we  shall  see,  its  own  Indirect  Method  falls 
outside  its  boundaries,  then  that  logic  does  not  give  the  true 
method  of  reasoning.  It  is  not  made  too  narrow  because  it 
requires  an  identity  underlying  the  terms  of  its  premises.  It 
is  made  too  narrow  because  in  its  conclusions  it  is  confined  to 
the  category  of  subject  and  attribute.  In  a  remarkable  pas- 
sage (Principles,  Ed.  II.  p.  22)  I  understand  Professor  Jevons 
to  admit  these  limitations.  His  logic,  so  far  as  it  exists  at 
present,  appears  to  be  confined  to  "simple  relations."  "A 
simple  logical  relation  is  that  which  exists  between  properties 
and  circumstances  of  the  same  object  or  class."  But,  if  that 
is  so,  then  the  theory  of  reasoning  will  cover  only  one  portion 
of  the  facts. 

§  II.  (4)  We  have  seen  that,  within  the  syllogistic  limits, 
equational  logic  will  work  very  well ;  and  we  also  have  seen 
the  nature  of  its  process.  However  right  it  is  to  insist  that  in 
reasoning  identity  is  necessary,  yet  exactly  the  same  must  be 
said  of  difference.  And  I  can  not  think  that,  in  laying  down 
his  principle  of  inference  and  in  reducing  it  to  a  formula, 
Professor  Jevons  has  avoided  serious  mistakes. 

"  So  far  as  there  exists  sameness,  identity  or  likeness,  what 
is  true  of  one  thing  will  be  true  of  the  other."  (^"  In  whatever 
relation  a  thing  stands  to  a  second  thing,  in  the  same  relation 
it  stands  to  the  like  or  equivalent  of  that  second  thing  "  (pp. 

9,  17).  ) 

Now  if  the  "  likeness  "  in  these  formulas  means  absence  of 
difference,  we  see  at  once  that  they  are  tautologous  or  false. 


not  do  at  all.  If  the  quantity  is  taken  in  abstraction  then  it  certainly  is 
the  same,  but  you  can  not  show  from  that  that  A,  B,  and  C  are  related  as 
equals  or  related  in  any  way.  But  if  you  take  the  quantity  in  its  relations 
to  A  and  B  and  C,  in  that  case  you  have  quaternio  termmorum,  or 
otherwise  the  premises  become  false.  The  relation  of  equality  never 
could  be  got  out  in  the  conclusion. 


Chap.  IV.]  JEVONS'   EQUATION AL   LOGIC.  351 

For  SO  far  as  mere  identity  exists,  what  is  true  of  any  one 
thing  must  for  that  very  reason  be  false  of  another.  If,  in  the 
case  of  A,  B,  and  C,  the  judgment  A-C  is  true  of  A  so  far  as  A 
is  simply  the  same  as  B,  then  it  either  is  not  true  of  A  at  all, 
or  else  the  differences  have  all  disappeared,  and  the  judgment 
oecomes  x=x.  So  again,  if  A  is  related  to  B,  it  is  related  to 
that  which  is  the  same  as  B.  But "  the  same  as  B  "  will  be 
simply  B,  and  we  have  not  advanced  one  single  step. 

§  12.  But  if  the  formulas  have  another  meaning,  then  what 
shall  we  say  that  their  meaning  is  }  They  certainly  can  not 
mean  that  mere  likeness  will  do.  A  need  not  be  like  C 
because  both  are  like  B.  And  it  is  obvious  that  if  B  and  C 
are  "  equivalent,"  A  need  not  stand  in  one  relation  to  both. 
Two  coins  are  equivalent  and  one  is  in  my  pocket,  but  neither 
logic  nor  fact  makes  me  master  of  the  other.  It  is  clear  that 
this  can  not  be  our  author's  meaning. 

The  equivalence  or  likeness,  to  be  that  which  is  meant, 
must  exist  to  a  sufficient  extent  or  degree.  But  what  is  the 
degree  which  is  sufficient  ?  "  The  general  test  of  equality  is 
substitution"  {Principles,  p.  19).  But  here  again  our  question 
is  not  answered.  It  would  never  do  to  say,  you  may  substi- 
tute when  you  have  a  sufficient  degree  of  likeness,  and  that 
degree  again  consists  in  your  ability  to  make  a  substitution. 
And  this  is  not  what  is  meant.  What  I  think  is  meant  is  that 
a  certain  amount  of  likeness  will  give  conclusions,  and  that 
when  you  can  substitute,  you  may  know  it  is  there.  But  I 
do  not  think  that  Professor  Jevons  has  anywhere  told  us  in 
what  that  degree  itself  consists. 

§  13.  Still  I  think  he  has  given  us  the  materials  for  an 
answer.  The  question  we  have  before  us  is  this.  Given  a 
term  B  in  relation  with  C  ;  or  otherwise,  Given  C  as  what  is 
true  of  B,  then  what  amount  of  sameness  between  A  and  B 
will  warrant  us  in  writing  A  for  B  ?  The  first  answer  to  be 
given  is  that  no  amount  is  wanted.  There  is  not  the  very 
smallest  need  for  A  and  B  to  be  like  or  equivalent.  But  the 
second  answer  to  be  given  is  this  :  the  sameness  required  is 
the  sameness  of  the  one  subject.  If  A  and  B  are  both 
qualities  of  X,  or  again  if  B  is  a  quality  of  A,  then  A  and  C 
will  be  interrelated.     The  quality  of  the  subject  is  the  middle 


352  THE    PRINCIPLES   OF   LOGIC.  [Bk.  XL  Pt.  II. 

term,  whose  predicates  in  some  way  qualify  the  subject.  Or  the 
identity  of  the  subject  is  the  middle  term  and,  so  far  as  this  iden- 
tity extends,  the  attributes  must  all  be  related  and  conjoined. 

We  have  finished  our  examination  of  the  theory  of  pro- 
positions, and  also  of  reasoning  by  substitution.  We  come 
now  to  a  third  and  most  important  point,  the  question  of  the 
Indirect  Method  and  the  Logical  Machine.  I  will  anticipate 
briefly  the  result  we  shall  reach,  {a)  The  essence  of  the 
Indirect  Method  is  a  process  which  can  not  possibly  be 
reduced  to  substitution,  {b)  In  part  of  that  process  substitu- 
tion may  be  used,  but  another  form  of  reasoning  is  just  as 
applicable,  {c)  The  Machine  will  not  really  give  complete 
conclusions,  {d)  It  is  improperly  limited  to  one  kind  of 
reasoning. 

§  14.  (C)  {a)  The  Indirect  Method  is  a  process  of 
exclusion.  In  using  it  you  must  first  find  all  the  possibilities, 
and  then  by  removal  of  the  rest  you  leave  only  one.  In 
other  words  you  have  a  disjunction,  and  remove  all  alter- 
natives except  a  single  remainder.  Because  the  subject,  if 
taken  as  real,  must  be  taken  as  fully  .determined  and 
particularized,  tJterefore  the  remaining  possibility  is  real  (cf. 
Book  I.  Chap.  IV.).  A  is  b,  c^  or  d :  it  is  not  b  ox  c  :  it  there- 
fore is  d.  This  is  the  essence  of  the  Indirect  Method,  and  we 
already  have  to  some  extent  made  its  acquaintance. 

§  15.  We  know  that  this  process  falls  outside  syllogism. 
And  from  that  we  might  argue  at  this  stage  of  our  enquiry 
that  it  can  not  be  reduced  to  substitution.  But  if  it  can  not  be 
reduced  to  substitution,  Professor  Jevons'  best  work  contradicts 
his  theory.     Let  us  see  how  he  tries  to  avoid  this  consequence. 

"  The  general  rule  is  that  from  the  denial  of  any  of  the 
alternatives  the  affirmation  of  the  remainder  can  be  inferred. 
Now  this  result  clearly  follows  from  our  process  of  substi- 
tution ;  for  if  we  have  the  proposition — 

A  =  B.|.C.|.D, 

and  we  insert  this  expression  for  A  on  one  side  of  the  self- 
evident  identity 

Kb=Kb, 
we  obtain  A^  =  AB^.|.  A^C-I- A^D  ; 


Chap.  IV.]  JEVONS'   EQUATION AL   LOGIC.  353 

and,  as  the  first  of  the  three  alternatives  is  self-contradictory, 
we  strike  it  out  according  to  the  law  of  contradiction ;  there 
remains  A*  =  A*C.|.A*D. 

Thus  our  system  fully  includes  and  explains  that  mood  of 
the  Disjunctive  Syllogism  technically  called  the  modus 
tolle?ido  poiiens  "  {Principles,  p.  "jj).  * 

But  this,  I  think,  will  not  stand  a  moment's  examination. 
In  the  first  place  the  operation  of  striking  out  one  part  and 
asserting  the  rest  is  the  essence  of  the  method,  and  yet  it  is  not 
even  in  appearance  reduced  to  substitution.  In  the  second 
place  in  this  example  the  reasoning  by  substitution  is  per- 
fectly useless.  It  does  not  bring  you  one  step  on  your  way 
towards  the  conclusion. 

I  will  take  a  perfectly  simple  instance. "  "  A  is  ^  or  <:,"  and 
"A  is  not  b!^  These  are  the  premises,  and  from  these  I 
should  say  that  you  go  directly  to  the  conclusion  "  A  is  ^." 
Professor  Jevons,  if  I  understand  him  rightly,  contends  that 
you  go  through  a  process  of  substitution.  K  —  b  oxc,K-=- not-b. 
Insert  the  expression  for  A,  "  A  is  ^  or  ^,"  on  one  side  of  A  not-/^ 
=  A  not-<^.  Then  A  not-<^,  =  A  not-^and  <^  or  A  not-^  and  c. 
But  A  not-^  and  ^  =  o,  therefore  A  not-^  =  o  or  wot-b  and  c. 

But  surely,  if  words  have  any  meaning,  when  I  know  that 
A  is  /^  or  c,  and  that  A  is  not  b,\  do  know  at  once  that  b 
must  be  removed.  And,  on  my  removing  b  by  an  ideal 
experiment,  c  by  itself  is  what  I  have  left.  If  I  please  I  may 
write  this  "r  or  o."  But  I  really  can  not  perceive  what 
advantage  I  get  by  turning  in  a  circle  to  come  back  to  my 
starting-place.  A  is  /^  or  c,  and  it  is  not  b.  If  possible  how- 
ever let  A  be  b.  But,  if  it  is  b,  it  will  be  b  and  not-^.  That 
is  impossible,  and  therefore  follows — what?  Why  simply 
that  A  is  not  b.  I  have  used  the  premise  to  prove  itself. 
And,  if  in  answer  I  am  told  that  this  is  not  so,  for  I  have 
enriched  what  was  given  me  by  the  alternative  "  or  o,"  then  it 
seems  to  me  that  I  may  fairly  reply.  If  you  do  not  know, 
given  only  b  and  c,  that  when  b  is  gone,  c  is  what  is  left  behind ; 
then  how  on  earth  can  you  tell  that,  given  "  c  or  o,"  when  o 

*  I  may  remind  the  reader  that  -J-  here  means  "or,"  and  b  means 
"  Not-B."    I  do  not  use  these  signs  in  the  text. 

2  A 


354  THE    PRINCIPLES   OF   LOGIC.  [Be.  IL  Pt.  II. 

is  gone,  c  is  all  that  is  left  ?  I  confess  to  me  one  is  no  clearer 
than  the  other. 

§  1 6.  What  I  think  has  occasioned  this  complete  mistake 
is  an  erroneous  idea  as  to  indirect  reasoning.  For  that  we 
must  have  a  disjunction  to  start  with,  and  by  removing  one 
member  we  prove  the  other.  And  we  gejierally  have  to  use 
direct  reasoning  downwards.  We  assume  as  one  of  our 
premises  that  alternative  which  we  want  in  the  end  to  get  rid 
of,  and  on  this  assumption  we  bring  out  a  conclusion  which 
contradicts  something  contained  in  the  premises.  This  is  the 
usual  course,  but  it  is  not  more  than  usual.  Direct  reasoning 
downwards  is  not  always  wanted.  For  when  the  premises 
themselves  give  the  removal  of  one  alternative,  what  more  can 
we  prove  by  such  direct  reasoning .?  W"e  have  in  our  hands 
not  only  the  disjunction,  but  also  the  exclusion  of  one  alternative. 
Where  direct  reasoning  is  required  it  is  simply  preliminary  to 
the  final  operation,  and  is  wanted  merely  to  prepare  the  sub- 
ject ;  and  when  the  premises  give  the  subject  ready  prepared, 
what  is  there  which  we  possibly  can  have  to  wait  for  ? 

And  I  think  this  mistake  is  connected  with  another.  I 
suspect  that  an  error  as  to  the  Laws  of  Contradiction  and 
Excluded  Middle  has  helped  to  lead  our  author  into  this 
pitfall.  But  when  we  know  that  the  Law  of  Excluded 
Middle  is  one  case  of  disjunction,  and  in  no  sense  the  basis 
of  it  (Book  L  p.  142),  we  see  at  once  that  no  mystical  force 
arises  from  the  proof  of  a  self-contradiction.  If  we  get  to  that 
by  turning  in  a  circle,  the  end  will  hardly  justify  the  means. 
It  has  no  power  to  absolve  our  consciences  from  the  ordinary 
sin  of  logical  fallacy. 

I  must  not  be  considered  as  wanting  in  respect,  if  I 
illustrate  what  I  mean  by  another  instance.  Suppose  that  my 
premise  is  "  A  is  b."  Will  any  one  deny  that  to  prove  from 
this  that  "  A  is  ^  "  is  a  frivolous  circle  }  But  it  is  easily  done. 
For,  if  possible,  suppose  that  A  is  not  b  ;  then  A  will  be  both 
b  and  not-<^  .•  or  insert,  on  one  side  of  the  self-evident  identity 
A  n©t-^  =  A  not-/^,  the  expression  for  A.  Then  A  not-^  =  A 
not-/^  and  b.  As  one  side  of  our  equation  is  now  self-contradic- 
tory, we  strike  it  out  according  to  the  law  of  contradiction,  and 
then  there  remains  A  not-/^  =  o,  or  K\?>  b.     I  must  be  allowed 


Chap.  IV.]  JEVONS    EQUATIONAL  LOGIC.  355 

to  state  my  conviction  that  this  circle  is  the  same  as  what  we 
had  above.  In  both  cases  alike  the  premise  has  been  used 
to  bring  out  nothing  whatever  but  that  which  it  gave. 

The  Indirect  Method,  we  so  far  have  seen,  can  not  be 
reduced  to  a  process  of  substitution. 

§  17.  {b)  If  we  consider  that  Method  as  employed  by 
Professor  Jevons,  it  does  make  use  of  the  equational  form,  but 
there  is  no  real  necessity  for  its  so  doing.  This  process 
consists  of  the  following  four  steps. 

"  I.  By  the  Law  of  Duality  develope  the  utmost  number  of 
alternatives  which  may  exist  in  the  description  of  the  required 
class  or  term  as  regards  the  terms  involved  in  the  premises. 

2.  For  each  term  in  these  alternatives  substitute  its 
description  as  given  in  the  premises. 

3.  Strike  out  every  alternative  which  is  then  found  to 
break  the  Law  of  Contradiction. 

4.  The  remaining  terms  may  be  equated  to  the  term 
in  question  as  the  desired  description "  {Pi'incipleSy  pp. 
89-90). 

The  one  part  of  this  process  which  employs  substitution, 
we  see,  is  the  second.  But  it  is  performed  just  as  well  by  the 
ordinary  method.  All  the  possible  combinations  of  the  terms 
are  given  us,  and  our  object  is  merely  by  means  of  the 
premises  to  remove  those  combinations  which  the  premises 
contradict.  In  what  shape  then  ought  we  to  have  our 
premises.?  Surely  one  would  say  in  the  shape  of -combina- 
tions. It  is  just  such  combinations  that  the  ordinary  process 
would  give  us  directly,  and  we  get  them  by  substitution  in  a 
roundabout  way.  For  the  "  description  "  of  the  term  is,  as  we 
saw,  the  judgment  we  make  about  the  term.  Hence  this  part 
of  the  method,  as  employed  by  Professor  Jevons,  is  valid  just 
so  far  as  it  can  be  stated  syllogistically.  For  the  premises 
are  combinations  of  attributes.  They  are  related,  as  Professor 
Jevons  says,  "just  as  the  qualities  of  the  same  object "  {ibid. 
p.  114);  and  if  they  were  anything  else,  his  method  could  not 
deal  with  them.  We  can  combine  them  directly,'if  we  please  : 
and  it  is  simply  our  choice,  and  perhaps  sometimes  our 
convenience,  if  we  combine  them  from  behind  through  their 
common  subject. 

2  A  2 


356  THE  PRINCIPLES  OF  LOGIC.  [Bk.  IL  Ft.  IL 

Thus  we  may  use  substitution  to  prepare  for  our  conclu- 
sion. But  we  can  not  use  it  to  draw  that  conclusion.  Its 
operation  ends  with  the  second  step. 

§  1 8.  We  see,  from  examining  the  method  itself,  that  it 
deals  with  syntheses  or  combinations,  and  does  not  deal  at 
all  with  equations.  And  the  method,  as  practically  worked 
with  the  machine,  confirms  the  truth  of  the  view  which  we  have 
taken.  Professor  Jevons  himself  with  the  greatest  candour 
has  called  attention  to  this  consideration. 

"  It  is  no  doubt  a  remarkable  fact  that  a  simple  identity 
can  not  be  impressed  upon  the  machine  except  in  the  form  of 
two  partial  identities,  and  this  may  be  thought  by  some 
logicians  to  militate  against  the  equational  mode  of  represent- 
ing propositions"  {Principles,  112). 

It  would  be  to  me  even  more  than  remarkable  if  the 
machine  could  work  with  simple  identities.  But  the  fact, 
which  Professor  Jevons  rightly  finds  remarkable,  has  I  think 
a  still  more  remarkable  counterpart.  The  conclusions  of  the 
machine,  if  I  understand  them  properly,  contradict  one 
another  when  read  as  equations  in  the  sense  of  assertions  of 
simple  identity.  A  —  B  —  C  is  consistent  with  Not-A  —  B  —  C  ; 
but  how  can  we  reconcile  A=  C  with  C  =  Not-A  } 

§  19.  (c)  We  come  now  to  the  subject  of  the  Logical 
Machine,  and  we  have  to  enquire  what  work  it  performs.  Of 
the  mechanism  employed  I  have  no  knowledge.  I  am  so 
incompetent  to  say  anything  about  it,  that  I  can  not  have  the 
pleasure  of  congratulating  Professor  Jevons  on  what  I  must 
believe  is  no  small  achievement.  But  what  the  machine  does 
perform  is  this.  All  the  possible  combinations  of  the  terms 
are  worked  out,  and  are  lying  ready  drawn  up  in  the  machine. 
The  operator  puts  in  at  one  end  his  premises,  each  in  the 
shape  of  a  combination.  The  combinations  of  these  premises 
remove  each  one  all  the  possibilities  with  which  it  is  irrecon- 
cileable.  And  what  comes  out,  so  to  speak,  at  the  other  end 
of  the  machine  is  all  the  residue  of  possible  combinations 
which  have  not  been  so  excluded  by  the  premises.  It  is  easy 
to  exaggerate  the  powers  of  the  machine.  But  I  think  it  is 
impossible  to  deny  that  it  executes  such  work,  as  must 
otherwise  be  done  by  a  process  of  thinking.     For  myself  I  do 


CiiAP.  IV.]  JEVONS'   EQUATIONAL   LOGIC.  35/ 

not  hesitate  to  say  that  it  performs  mechanically  an  operation 
which,  if  performed  ideally,  would  be  an  inference.  And  in 
this  sense  I  think  Professor  Jevons  is  justified  in  his  claim  to 
have  made  a  reasoning  machine.  Apart  from  the  practical 
utility  of  the  instrument,  which  in  certain  cases  may  be 
considerable,  we  must  admit  that,  from  a  merely  theoretical 
point  of  view,  it  is  a  most  interesting  and  instructive  phe- 
nomenon. If  Professor  Jevons  had  made  no  other  contribu- 
tions to  logic,  we  might  yet  be  sure  that  his  name  would  go 
down  with  the  history  of  the  science. 

But  to  say  on  the  other  hand  that  the  machine  will  execute 
the  whole  process  our  minds  perform  in  the  inference — that 
the  raw  material  goes  in  at  one  side,  and  the  finished  con- 
clusion comes  out  at  the  other,  would  be  travelling  far  beyond 
the  fact.  Before  the  premises  can  be  worked  on  the  instrument, 
thay  have  of  course  to  be  reduced  and  formulated,  so  as  to 
take  the  shape  of  combinations  of  letters.  But  this  is  not 
the  most  important  point.  The  result  that  comes  out  and  is 
presented  by  the  machine,  is  not  really  the  conclusion.  The 
process  is  not  finished  when  the  machinery  stops  ;  and  the 
rest  is  left  to  be  done  by  the  mind.  What  is  called  "  reading'' 
the  conclusion  is  to  some  extent  making  it. 

§  20.  I  will  explain  what  I  mean.  In  the  machine  is 
drawn  up  a  complete  disjunction  of  the  possible  arrangements 
of  those  terms  which  we  employ.  Before  we  begin  to  work 
the  problem  the  machine  thus  supplies  us  with  one  of  our 
premises.  It  states  all  possibilities,  and  this  is  its  strength. 
But  it  states  mere  possibilities,  and  this  is  its  weakness.  We 
begin  our  operation,  and  insert  the  combinations  which  are 
given  us  by  our  data.  These  combinations  are  the  rest  of  the 
premises.  The  machine,  as  it  receives  each  combination, 
removes  from  the  list  of  all  the  possibilities  those  which  are 
inconsistent  with  this  datnm.  Then  the  remainder  of  the 
possible  combinations  are  exposed.  But  they  still  remain  bare 
possibilities,  and  are  never  stated  as  actual  facts. 

The  process  may  be  taken  as  having  five  parts,  i.  The 
complete  disjunctive  statement  of  possible  combinations. 
This  is  given  ready-made  by  the  machine.  2.  The  reduction 
of  the  premises  to  the  shape  of  combinations.     This  is  done 


358  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IL  Ft.  II. 

entirely  by  the  operator.  3.  The  discovery  of  those  alterna- 
tives which  are  inconsistent  with  the  combinations  of  the 
premises.  This  step  is  performed  entirely  by  the  machine. 
4.  The  removal  of  those  alternatives.  This  step  again  is 
performed  by  the  machine,  and  it  is  the  first  part  of  that  final 
inference  which  gives  the  conclusion.  5.  The  assertion  that 
what  is  left  is  true,  and  that,  if  but  one  possibility  remains, 
that  is  fact.  This  is  absolutely  necessary  to  complete  the 
inference,  and  this  is  done  entirely  by  the  operator. 

The  final  step  may  seem  to  some  persons  a  final  super- 
fluity. But  on  that  view  of  the  nature  of  reasoning  by  way 
of  the  exclusion  of  alternatives  which  has  seemed  to  me 
true,  it  is  integral  and  essential.  Yet  it  can  not  be  said  to  be 
performed  by  the  instrument. 

§  21.  I  wish  to  stand  on  this  statement  of  the  case.  But 
it  is  possible  to  use  also  an  argtmienttim  ad  hominem.  If  the 
too  undiscriminating  friends  of  the  ,  machine  assert  that  its 
result  is  a  categorical  statement,  they  can  hardly  fail  to  com- 
promise it  deeply.  They  will  make  it  an  instrument  for  the 
production  of  falsehoods.  Let  us  take  one  result  that  is  given 
by  the  machine  (Principles,  109). 

A-B-C.  NotA-B-C. 

NotA-notB-C.  Not  A- not  B- not  C. 

Now,  there  being  here  but  one  possibility,  if  A  is  assumed, 
we  are  practically  safe  in  contending  that  the  machine  cate- 
gorically asserts  this  one  possibility.  But  suppose  we  take 
the  same  line  throughout,  we  plunge  at  once  into  a  sea  of  non- 
sense. Contradictory  possibilities  can  co-exist  as  long  as  they 
remain  mere  possibilities,  but  the  moment  you  affirm  them 
as  actual  fact,  they  exclude  one  another.  And,  if  so,  either 
the  machine  brings  out  false  conclusions,  or  all  must  be  read 
as  mere  possibilities.  You  have  no  warrant  from  the  machine 
for  the  assertion  Kis  Q.  A  may  be  C  ;  and  because  it  may 
be,  and  because  there  is  nothing  else  that  it  may  be,  and 
because  you  know  that  it  must  be  something  to  C  one  way  or 
the  other,  you  therefore  ijifer  that  A  is  C,  a  conclusion  not 
given  to  you  by  the  machine. 

§  22.  {d)   The  machine  performs   more  than  we   have  a 


GiiAP.  IV.]  JEVONS    EQUATIONAL   LOGIC.  359 

right  to  ask,  and  it  is  a  pity  to  credit  it  with  fictitious  powers. 
We  have  seen  that  it  does  not  bring  out  a  conclusion.  But  it 
is  Hmited  beside  in  another  respect.  Although  it  does  not 
work  by  substitution,  yet  its  range  is  limited  to  that  kind  of 
inference  which  is  possible  in  equational  logic  or  in  syllogism. 
It  can  hot  deal  with  any  other  combinations  than  those  which 
represent  the  co-existence  of  qualities  within  a  subject.  And 
this  is  a  very  serious  defect ;  for  it  means  that  the  machine 
refuses  to  touch  more  than  a  part  of  the  subject. 

This  is  not  the  fault  of  the  Indirect  Method  itself.  Apart 
from  restrictions  artificially  imposed  on  it,  that  is  applicable 
everywhere  and  to  all  kinds  of  matter.  If  my  premises  are 
"  A  is  to  the  right  of  B,  and  B  of  C,"  I  may  go  directly  from 
these  to  my  conclusion  ;  but,  if  I  choose,  I  may  use  the 
indirect  method.  The  possibilities  of  A  with  respect  to  C  are 
either  absence  of  any  spatial  relation,  or  A  to  the  right  of  C,  or 
to  the  left  of  C,  or  neither  and  above  it,  or  below  it,  &c.  But  the 
premise  "  A  to  the  right  of  B,"  will  exclude  (as  we  should  see  by 
an  ideal  construction)  every  alternative  w-e  can  find  other  than 
A  to  the  right  of  C.  For,  if  we  assumed  any  one  of  the  others, 
we  should  bring  out  a  result  incompatible  with  our  premise. 
The  remaining  possibility  is  therefore  fact.  This  is  perfectly 
familiar  and  common-place  reasoning,  and  a  system,  in  which  it 
can  find  no  place,  must  assuredly  be  called  at  least  incomplete. 

§  23.  The  result  of  our  perhaps  too  brief  examination  may 
be  stated  as  follows  : — 

1.  The  Indirect  Method  has  absolutely  no  vital  connection 
with  the  Substitution  of  Similars. 

2.  That  Method  itself  is  flawless  and  complete,  but  as  used 
by  Professor  Jevons  it  is  improperly  limited. 

3.  The  machine  which  works  within  these  limits  will  not 
actually  give  a  categorical  conclusion. 

4.  These  unfortunate  limits  are  also  those  of  equational 
reasoning. 

5.  They  coincide  exactly  with  the  boundary  of  the  syllo- 
gism, and  a  large  part  of  reasoning  falls  entirely  without  them. 

6.  The  method  of  Substitution  is  syllogism  upside  down, 
and  its  principle  has  not  been  accurately  formulated  by  Pro- 
fessor Jevons. 


36o  THE  PRINCIPLES   OF  LOGIC.  [Bk.  II.  Pt.  U. 

I  must  leave  this  subject  with  an  expression  of  regret.  I 
am  sorry  to  have  had  no  more  space  available  ;  and  I  am 
sorry  to  have  dwelt  almost  wholly  on  those  points  in  which  I 
am  unable  to  follow  the  author.  It  would  have  been  more 
pleasant,  if  it  had  been  possible,  to  have  called  attention  to 
the  various  merits  of  his  logical  work.  But  still,  even  if  my 
praises  could  do  him  any  service,  fortunately  he  does  not 
stand  in  need  of  them.  I  may  end  this  chapter  by  expressing 
my  belief,  that  no  living  Englishman  has  done  one  half  the 
service  to  logic  that  Professor  Jevons  has  done.  No  living 
writer,  to  the  best  of  my  knowledge,  now  Professor  Lotze  is 
dead,  has  done  more.  Personally  to  myself,  and  so  far  as  my 
own  studies  are  concerned.  Professor  Jevons'  book  has  been 
of  very  great  use  ;  and  I  could  not  truly  say  that  of  any  other 
English  Logic.  It  is  not  inability  to  accept  conclusions  which 
prevents  one  learning.  And  there  can  not  be  any  one  who  has 
left  unread  the  Principles  of  Science,  who  has  not  something  to 
learn  from  it.* 


*  Since  this  chapter  was  written  Professor  Jevons'  lamented  death 
has  taken  place,  and  has  deprived  me  of  any  opportunity  I  might  other- 
wise have  had  of  learning  from  him  in  what  points  I  have  failed  to  under- 
stand his  doctrines.  I  have  thought  it  best  to  leave  the  chapter  as  it 
stood. 

But  there  is  another  point  on  which  the  reader  may  look  for  some 
explanation.  He  may  ask  why  I  have  failed  to  examine  one  of  those 
views  of  Equational  Logic  which  treat  the  subject  mathematically. 
And  I  am  compelled  to  throw  the  burden  of  the  answer  on  those  who 
had  charge  of  my  education,  and  who  failed  to  give  me  the  requisite 
instruction.  It  would  have  been  otherwise  a  pleasure  to  have  seen  how 
the  defects  of  the  Equational  theory  appeared  in  a  mathematical  form. 
For,  at  the  risk  of  seeming  no  less  prejudiced  than  ignorant,  I  am  forced 
to  state  the  matter  so.  If  I  knew  perhaps  what  Mathematics  were,  I 
should  see  how  there  is  nothing  special  or  limited  about  them,  and  how 
they  are  the  soul  of  logic  in  general  and  (for  all  I  know)  of  metaphysics 
too.  Meanwhile  Cl  may  suggest  to  the  mathematical  logician  that,  so 
long  as  he  fails  to  treat  (for  example)  such  simple  arguments  as  "A  before 
B,  and  B  with  C,  therefore  A  before  C,"  he  has  no  strict  right  to  demand 
a  hearing.*^  Logic  is  not  logic  at  all  if  its  theory  is  based  on  a  previous 
mutilation  ^of  the  facts  of  the  subject.  It  may  do  something  which 
perhaps  is  very  much  better,  but  it  does  not  give  any  account  (adequate 
or  inadequate)  of  reasoning  in  general.  And  at  the  risk  of  exhibiting 
prejudice  once  more,  I  may  say  that  this  consideration  seems  to  me 
to  be  vital. 


BOOK    III.— PART    I 

INFERENCE    CONTINUED, 


CHAPTER  I. 

THE  ENQUIRY   REOPENED. 

§  I.  In  the  Second  Part  of  the  foregoing  Book  we  were 
concerned  with  negations.  We  were  employed  in  banishing 
some  views  of  inference  which  appeared  erroneous.  From 
this  negative  process  we  turn  with  reHef,  and  with  the  hope  of 
rest  in  a  positive  result.  But  we  must  not  deceive  ourselves. 
The  positive  result  we  have  already  reached,  offers  a  welcome 
in  part  illusive,  and  a  rest  that  is  doomed  to  speedy  dis- 
turbance. We  saw  in  all  inference  an  ideal  synthesis,  which 
united  round  a  centre  or  centres  of  identity  not  less  than  two 
terms  into  one  construction.  The  conclusion  was  then  a  new 
relation  of  these  terms,  and  it  was  by  an  intuition  that  we 
perceived  it  to  exist  within  the  individual  whole  we  had 
compacted.  And  this  account  that  we  gave  was  not  a  false 
account,  for  it  was  true  of  those  inferences  to  which  we 
applied  ourselves.  But  there  are  other  reasonings  no  less 
important,  which  we  then  ignored,  and  which  fall  beyond  it. 
It  was  thus  a  theory  provisional  and  limited  in  range. 

§  2.  And  there  came  a  point  where  we  had  to  transcend 
it.  In  negative  inference  we  were  forced  to  contemplate  the 
possibility  of  retaining  the  middle  (Book  II.  Part  I.  V.  §  8).  If, 
our  construction  being  reached,  we  choose  to  rest  in  it,  if  we 
refuse  to  isolate  a  single  relation  within  that  whole,  if  we  prefer 
to  treat  the  entire  compound  synthesis  as  the  conclusion  we 
want,  are  we  logically  wrong }  Is  there  any  law  which 
orders   us   to   eliminate,  and,  where   we   can   not  eliminate. 


3^2  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

forbids  us  to  argue  ?  The  question  once  asked  is  its  own 
reply,  and  it  rings  the  knell  of  a  blind  superstition  which 
vanishes  in  daylight. 

If  so,  we  have  been  forced  beyond  our  formula.  For  the 
conclusion  is  not  always  a  new  relation  of  the  extremes  ;  it 
may  be  merely  that  interrelation  of  the  whole  which  does  not 
permit  the  ideal  separation  of  a  new  relation.  And,  having 
gone  so  far,  we  are  led  to  go  farther.  If,  the  synthesis  being 
made,  we  do  not  always  go  on  to  get  from  that  a  fresh 
relation,  if  we  sometimes  rest  in  the  whole  we  have  con- 
structed, why  not  sometimes  again  do  something  else } 
Why  not  try  a  new  exit }  There  are  other  things  in  the 
world  besides  relations ;  we  all  know  there  are  qualities,  and 
a  whole  put  together  may  surely,  if  not  always  at  least 
sometimes,  develope  new  qualities.  If  then  by  construction 
we  can  get  to  a  quality,  and  not  to  a  relation,  once  more  we 
shall  have  passed  from  the  limit  of  our  formula. 

§  3.  The  next  Chapter  will  show  that  this  kind  of 
inference  really  exists,  but  at  present  we  must  follow  the  lead 
of  those  doubts  which  it  tends  to  awaken.  If  our  formula  is 
not  wide  enough,  and  if  we  framed  it  to  suit  the  facts  we  had 
before  us,  it  is  natural  to  suspect  those  facts  we  trusted  in. 
Are  they  complete  ?  Are  there  not  other  inferences,  which 
we  failed  to  consider,  and  which,  if  we  considered  them, 
would  affect  the  result  ?  And  this  question  once  asked  leads 
to  consequences  we  hid.  Though  we  widened  our  facts 
beyond  the  boundary  of  the  traditional  logic,  we  stopped 
short  of  the  truth.  We  desired  to  inveigle  by  doubtful 
promises,  and  commit  the  reader  to  a  voyage  he  could  not 
easily  be  quit  of  We  are  now  at  sea  where  alarm  brings  no 
risk,  and  we  may  avow  the  truth  that,  in  our  former  account, 
we  left  out  a  very  great  part  of  the  subject.  There  are  large 
branches  of  reasoning  which  we  deliberately  ignored,  and 
which  explode  the  formula  we  went  on  to  set  up.  The 
following  Chapter  will  detail  their  nature,  and  we  may 
content  ourselves  here  with  a  brief  enumeration. 

§  4.  Our  education  in  logical  superstition  leads  us  first  to 
think  of  Immediate  Inferences.  Are  they  provided  for? 
The  syllogism  itself  perhaps  failed  to  provide  for  them,  but 


CuAP.  I.]  THE   ENQUIRY  REOPENED.  363 

the  failure  of  the  syllogism  can  not  be  our  excuse.  No  doubt 
we  might  appropriate  the  doctrines  advanced  by  some 
enemies  of  tradition,  and  reply  that  the  so-called  Immediate 
Inferences  are  not  inferences  at  all,  and  that  we  are  not 
required  to  provide  specially  for  illusions.  But  I  do  not 
think  that  this  answer  will  hold.  If  some  immediate 
inferences  seem  to  be  tautologies,  yet  others  are  more 
stubborn.  They  appear  to  get  to  a  fresh  result,  and  they 
certainly  do  not  seem  to  move  in  accord  with  our  formula. 

§  5.  We  have  now  begun  the  list  of  our  difficulties,  and  it 
does  not  much  matter  how  we  proceed  with .  it.  We  may 
take  up  next  the  operations  of  Arithmetic.-  Addition  and 
subtraction  seem  processes  of  reasoning,  but  they  scarcely 
can  be  said  to  present  a  new  relation  of  extremes  existing  by 
virtue  of  relation  to  a  middle.  So  too  with  Geometry  :  when 
I  prove  equality  by  ideal  superposition,  is  this  no  reasoning 
and  no  kind  of  inference  .?  On  the  other  hand  does  it  show 
that  terms  are  related  because  of  a  common  relation  to  a 
third  term  ?  However  in  the  end  we  may  answer  this 
question,  it  certainly  seems  to  suggest  a  problem  which  we 
took  no  account  of  Our  formula  once  more  perhaps  is  not 
adequate. 

§  6.  Then  come  other  difficulties.  When  A  is  given  us, 
and  we  are  able  to  find  two  further  possibilities,  Ab  and  Acy 
and  when  again  some  other  knowledge  assures  us  that  A^  is 
not  real — on  this  we  assume  that  Ab  is  fact.  We  seem  here 
to  reason,  and  to  reason  with  at  least  a  show  of  correctness, 
but  the  form  of  our  inference  is  not  provided  for.  Even  if 
we  assume  that  it  can  be  reduced  to  the  type  we  have 
acknowledged,  the  reduction  is  at  least  a  task  we  have  not 
yet  taken  in  hand.  And  the  reduction  may  possibly  prove 
not  practicable. 

§  7.  We  are  not  at  an  end.  When  an  object  AB  is 
recognized  as  C,  the  C  is  added  by  ideal  supplement,  and  we 
seem  to  have  a  genuine  inference.  But  this  inference  has  not 
got  the  premises  we  required.  In  the  cases  which  we  con- 
sidered the  premises  were  data,  but  we  see  here  no  dattim  be- 
yond the  perception.  This  is  once  more  a  ground  for  amending 
our  formula.      And  then  again  we  seem  to  find  yet  another 


3^4  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Ft.  L 

ground  in  the  hypothetic  judgment.  Imagine  A,  and  per- 
haps nothing  follows  :  but  suppose  A  real,  and  we  may  then 
seem  compelled  to  get  A-B.  This  operation  suggests 
enquiry,  and  it  leads  us  to  think  of  yet  another  trouble.  In 
the  method  of  Dialectic  a  result  is  got  by  an  ideal  opera- 
tion, which  hardly  consists  in  the  act  of  putting  terms 
together.  Now  it  may  be  said  that  the  method  is  a  pure 
illusion,  but  that  short  way  would  perhaps  prove  long  in  the 
end,  and  would  lead  to  enquiries  not  easy  to  dispose  of.  It 
is  better  in  the  interest  of  logic  to  ask  under  what  type  of 
reasoning  this  method  will  fall  ;  a  question  which  once  more 
may  cause  a  strain  in  the  fabric  of  our  formula. 

§  8.  If  ideal  operations  which  lead  to  fresh  judgments  all 
claim  to  be  inferences — and  this  claim,  we  may  be  sure,  will 
now  be  set  up — we  shall  have  to  consider  some  other  questions 
which  we  before  ignored.  Take  first  Abstraction ;  here  an  opera- 
tion of  analysis  is  performed  on  some  datum^  and  in  conclusion 
a  judgment  is  got  which  is  concerned  with  one  element  of 
the  original  whole.  Is  this  judgment  which  we  thus  have 
reached  a  conclusion }  And,  if  it  is  a  conclusion,  will  the 
reasoning  fall  under  the  type  which  we  recognize  ?  There  is 
matter  here  for  doubt  and  discussion,  and  the  discussion  seems 
likely  to  carry  us  further.  For  in  Comparison  and  Distinction 
we  get  to  results,  and -and.  we  get  to  them  by  an  ideal  experi- 
ment. Is  that  experiment  inference  ?  If  so,  we  once  more 
are  asked  to  what  type  the  inference  conforms.  We  may 
already  and  by  anticipation  have  provided  a  place  for  it,  but 
appearances,  I  confess,  are  much  against  us.  We  can  not  off 
hand  dismiss  the  claim  set  up  by  these  processes,  and  we 
can  not  easily  bring  them  under  our  formula. 

§  9.  It  is  clear  that  our  hope,  if  we  had  any  hope,  of  a 
speedy  termination,  must  now  be  relinquished.  We  must 
prepare  ourselves  to  reopen  our  enquiry  as  to  the  general 
nature  of  the  reasoning  process.  The  next  Chapter  must  go 
through  the  mental  operations  we  have  here  enumerated.  It 
will  ask  first  if  they  really  are  inferences,  and  will  next  discuss 
the  peculiar  nature  of  each.  From  this  basis  we  may  hope  to 
arrive  in  the  end  at  some  positive  result. 


(     365 
CHAPTER  11. 

FRESH   SPECIMENS   OF  INFERENCE. 

§  I.  In  the  preceding  Book  we  possessed  an  advantage  we 
no  longer  enjoy.  Those  examples  of  reasoning,  upon  which  we 
worked,  were  too  clear  to  be  doubted.  No  unprejudiced  mind 
could  deny  the  fact  of  their  being  inferences,  and  the  issue  was 
confined  to  the  question  of  their  principle  and  inner  nature. 
But  at  the  point  which  we  have  reached,  doubt  is  possible  on 
all  sides.  Not  only  will  the  character  of  the  specimens  we 
produce  be  matter  of  debate,  but  their  claim  to  be  specimens 
will  be  disallowed.  We  must  ask  not  merely.  To  what  kind 
of  inferences  do  they  belong,  but,  Are  they  really  inferences 
at  all  ? 

With  this  prospect  in  sight  a  preliminary  reflection,  before 
we  argue,  seems  likely  to  be  useful.  What  test  shall  we  apply, 
when  any  claim  to  inference  is  sent  in  .?  Where  the  facts  are 
not  palpable  it  will  clearly  be  a  gain  if  we  are  able  to  agree  to 
an  explicit  Canon,  for  we  then  shall  have  something  to  which 
we  can  appeal  in  the  course  of  the  discussion. 

§  2.  We  may  say  that  inference  is  the  same  as  reasoning, 
that  to  reason  without  inferring,  or  to  infer  without  reasoning, 
does  not  sound  possible.  But  when  do  we  reason  ?  Do  we 
always  reason  wheA  a  judgment  is  given  as  a  judgment  for 
which  we  have  a  reason  ?  If  that  reason  were  taken  as  a  fact 
merely  got  by  simple  perception,  then  this  question  would 
probably  be  answered  in  the  negative.  But  suppose  our  reason 
is  no  fact  of  sense,  but  is  another  judgment  ;  not  something 
that  exists  but  some  knowledge  that  we  have  of  it — the  answer 
surely  will  in  that  case  be  different.  We  should  be  said  to 
reason  where  a  truth  is  given  as  a  reason  for  belief  in  another 
truth.  In  other  words  where,  instead  of  affirming  that  S  is  P, 
we  say  S  must  be  P,  wherever  we  have  a  necessary  truth,  there 


3^6  THE   PRINCIPLES   OF  LOGIC.  [Bk.  IIL  Pt.  I. 

is  reasoning  and  inference.  We  apply  the  same  test  in  a. 
different  form  when  we  turn  to  the  use  of  "why"  and 
"  because."  If  these  have  a  sense,  if  it  is  possible  to  ask  Why, 
and  then  to  answer  Because,  in  all  such  cases  we  seem  to  have 
an  actual  inference.  There  is  judgment  as  to  which  a  doubt 
can  be  raised,  and  that  doubt  is  satisfied,  not  by  pointing  to  a 
fact,  but  by  reference  to  a  truth.  There  is  a  mental  operation, 
in  which  a  result  is  seen  to  follow  from  an  ideal  datum.  And 
we  may  agree  that  wherever  this  mark  exists,  an  inference  is 
'present. 

§  3.  And  there  is  another  mark  which  perhaps  we  may  use. 
Where  illusion  exists  it  seems  to  arise  from  mistaken  inference  ; 
fo"r  the  senses  are  infallible  because  they  do  not  reason,  and 
fallacy  can  come  from  nothing  but  inferring.  If  this  is  true, 
then  possibility  of  error  means  presence  of  inference,  and  we 
may  employ  the  first  as  a  test  of  the  second'.  But  we  are 
treading  here  upon  dangerous  ground.  It  may  be  denied  that, 
when  water  is  hot  to  one  hand  and  cold  to  the  other,  the 
mistake  that  exists  is  a  fallacy  of  inference  ;  and  the  denial 
could  not  well  be  discussed  in  these  pages.  We  can  not  assume 
that  in  every  case  where  error  is  possible,  reasoning  exists, 
and  so  we  are  disappointed  in  our  canon  ;  but  for  all  that  we 
have  an  admitted  indication.  It  will  be  agreed  that,  where 
we  discover  mistake,,  we  shall  not  be  wrong  in  looking  for 
inference,  and  that,  to  some  extent  at  least,  we  may  expect  to 
find  it. 

§  4.  Armed  with  this  understanding  we  may  begin  at  once, 
and  may  take  up  the  claims  which  our  first  Chapter  found 
were  demanding  a  scrutiny.  They  make  no  pretence  to 
exhaust  the  array  of  possible  applicants,  and  they  enter  in  no 
systematic  order.  Still  we  hope,  and  believe,  that  the  worst 
has  shown  itself,  and  we  at  least  do  not  know  of  more  terrors 
in  the  background. 

(A)  The  first  to  come  in  are  the  three-term  constructions ; 
(i)  those  where  elision  is  simply  not  used,  and  (ii)  those 
operations  where  we  also  go  to  a  quality.  What  reply  shall  we 
make  to  each  of  these  ? 

(i)  I  cannot  think  of  any  way  by  which  to  escape  the  claim 
of  the  first.     If  A  is  given  to  the  right  of  B,  and  B  again  to 


CiiAP.  II.]  FRESH   SPECIMENS  OF  INFERENCE.  367 

the  right  of  C,  and  I  therefore  judge  that  the  terms  are 
arranged  as  C  —  B  —  A,  this  is  clearly  an  inference.  I  did  not 
know  it  before,  and  I  get  it  by  putting  two  truths  together. 
And  if  this  is  not  an  inference,  why  is  it  an  inference  when  I 
go  to  C  —  A  ?  No  answer  can  be  given  ;  we  are  forced  to 
admit  that  C  —  B  —  A^is  inferred  ;  and  yet  it  is  not  an  inference 
according  to  our  formula. 

§  5.  (ii)  But  there  follows  close  a  further  consequence.  We 
have  reasoned  to  a  whole  C  —  B  —  A,  and  this  whole  may  have 
a  new  quality  x.  But,  if  so,  we  have  reasoned  from  terms  in 
relation,  C  —  B  and  B  —  A,  to  no  new  relation  but  to  the  presence 
of  a  fresh  quality;  and  hence  once  more  our  formula  has 
broken  down. 

A  friend  of  our  youth  may  be  called  upon  here  to  supply 
us  with  an  instance.  I  sail  round  land,  and  reconstruct  my 
course  by  a  synthetic  process,  and  the  whole  shore  that  I  com- 
bine is  then  interpreted  as  belonging  to  an   island.     A  — B, 

H     A 


B-C,  C-D,D-F,  F-H  become,  when  united,  F <  >B  ; 


D  Q 
and  from  this  circular  frontage  I  go  to  the  name  and  to  the  other 
qualities  possessed  by  islands.  I  may  be  told  in  reply  that  the 
name  and  the  qualities,  if  indeed  there,  are  such,  do  not  come 
directly  from  the  construction  itself,  but  are  got  by  a  further 
and  additional  premise  that  does  not  appear.  And  this,  I 
admit,  is  true  altogether  of  the  name,  and  true  in  part  of  the 
other  qualities.  But  it  still  leaves  something  which  comes  from 
the  construction,  and  which  comes  directly.  The  circular  shape 
and  self-contained  singleness  afe  more  than  the  mere  inter- 
relation of  the  premises,  and  need  not  be  got  from  previous 
knowledge  of  islands.  You  do  not  go  outside  the  construction 
to  get  them,  the  whole  would  not  be  itself  without  them  ;  and 
yet  they  are  another  side  of  that  whole,  which  is  distinct  from 
the  putting  together  of  the  parts.  But,  if  so,  surely  you  have 
reasoned  to  a  quality. 

At  some  time,  I  presume,  we  have  all  been  visited  with  the 
pleasing  pain  of  hanging  our  pictures  and  arranging  our 
furniture.     How  many  combinations  were  we  forced  to  reject, 


368  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

until  we  came  upon  one  which  would  do.  But  these  attempts 
were  all  inferences  from  hypothetical  data^  and  we  went  from 
the  construction  direct  to  a  quality,  and  so  to  a  judgment.  If 
the  quality  was  aesthetic  that  made  no  difference  ;  for  we  did 
not  say  of  the  whole  psychological  image,  That  now  hurts  me, 
or  gives  me  a  pleasant  sensation.  We  said  of  the  content, 
which  we  had  in  the  premises.  That  leads  and  must  lead  to  a 
certain  result.  And  this  was  an  inference,  which  certainly  fell 
outside  our  formula. 

It  is  clear,  I  think,  that  when  trying  experiments  in  the 
actual  world  by  combining  and  dividing  real  things,  or  by 
drawing  upon  paper,  we  may  be  surprised  by  qualities  which 
we  did  not  anticipate.  And  the  same  must  be  true  of  ideal 
experiment.  In  both  cases,  the  interrelation  being  given,  we 
perceive  a  quality  which  comes  from  that,  and  which  is  more 
than  and  beyond  the  bare  interrelation.  But  in  the  second 
case  the  construction,  being  got  by  an  ideal  process,  is  itself  an 
inference,  and  its  result  is  also  nothing  but  a  conclusion.  But 
it  is  not  any  fresh  relation  of  the  original  data  ;  it  is  an  issuing 
quality. 

§  6.  It  seems  clear  that  reasoning  does  not  always  give  us 
a  new  relation  of  the  terms  we  began  with.  Our  formula  has 
now  too  palpably  lost  its  virtue ;  and  virtue  being  gone,  we 
may  proceed  less  anxiously.  The  advances  of  those  more 
audacious  claimants,  who  showed  their  heads  in  the  foregoing 
Chapter,  may  be  calmly  received.  There  is  no  longer  any 
absolute  presumption  against  them,  and  the  reception  of  each 
is  a  matter  not  of  principle,  but  of  choice  and  convenience. 

(B)  In  this  spirit  we  may  meet  the  approaches  of  Arithmetic, 
the  claim  of  which  I  will  bring  in  indirectly.  An  introduction 
is  certainly  not  required,  but  it  may  serve  to  make  the  change 
less  startling. 

We  saw  long  ago  that,  when  spatial  relations  with  points 
of  identity  were  forced  on  our  attention,  we  could  put  them 
together  and  find  a  new  relation.  We  have  lately  seen  that, 
instead  of  a  relation,  these  premises  could  supply  us  with  an 
unknown  quality.     Given  linqs  A  — B,  B-C,  C  — A,  we  can 

A 
construct  t>/\/-    and  from  that  construction  get  the  quality 


Chap.  II.]  FRESH   SPECIMENS   OF   INFERENCE.  369 

possessed  by  a  certain  triangle.  In  this  case  the  conclusion  is 
categorical  and  necessary. 

But  there  was  something  else  which  we  hardly  glanced  at. 
We  may  have  three  lines  such  as  A  —  B,  C  —  D,  E  —  F.  In 
these,  as  they  are  given  us,  there  are  no  points  marked 
identical,  and  we  have  no  given  reason  for  putting  them 
together.  But  we  may  do  so  if  we  choose  ;  if  their  lengths  do 
not  forbid  it,  we  may  arrange  them  ideally,  combining  them  into 
the  form  of  a  triangle,  and  thus  endowing  them  with  a  certain 
quality.  We  have  here  an  intuition  which  follows  on  a  syn- 
thesis, and  the  doubt  which  arises  is.  Have  we  an  inference  ? 

If  we  have  one  what  is  it }  It  is  not  "  AB,  CD,  EF  have 
X.''  That  would  be  false,  since  they  a7^e  not  combined,  and 
since  they  /lavenot  together  any  quality  at  all.  And  again  the 
inference  can  not  run  thus,  "  AB,  CD,  EF,  when  their  terminal 
points  are  identified,  have  x."  That  certainly  is  true,  but  then 
it  is  not  an  inference.  For,  though  the  quality  is  perceived  in 
an  ideal  arrangement,  it  has  not  been  got  by  it.  The  combi- 
nation in  this  case  would  not  be  such  a  construction  as  was 
made  to  get  the  judgment,  and  therefore  connects  the  judg- 
ment with  the  original  data.  The  judgment  is  passed  on  a 
whole  that  is  found,  and  it  says  nothing  about  tlie  ideal  com- 
position of  that  whole.  And  for  ^  this  reason  it  can  not  be  a 
conchision. 

The  real  conclusion  is  "  AB,  CD,  EF  may  be  combined, 
and  when  combined  they  have  a  quality;ir,"  or  "If  AB,  CD, 
EF  are  manipulated  in  a  certain  way,  they  give  rise  to  x^ 
The  lines  phis  my  arranging  activity  are  the  premises,  and  the 
construction  with  its  quality  follows. 

This  has  all  the  marks  of  inference,  but  it  obviously  differs 
from  the  inference  we  got  from  A  — B,  B  — C,  C— A.  In 
this  case  the  construction  follows  from  the  data  themselves, 
but  in  the  other  example  it  does  not  follow,  unless  an  arbi- 
trary arrangement  of  my  own  is  added.  My  free  manipu- 
lation has  taken  the  place  of  the  compulsory  synthesis  through 
identity  of  the  terminal  points  B,  C,  A.  The  lines  need  not 
have  any  point  that  is  identical,  and  I  am  not  obliged  to  put 
them  together.  The  premises  are  hypothetical,  and  the 
conclusion  is  thus  arbitrary.     But  it  still  is  an  inference,  for  if 

2  B 


370  THE   PRINCIPLES  OF   LOGIC.  [Bk.  III.  Pt.  I. 

the  lines  are  combined,  then  the  quaUty  must  come  because 
they  are  combined. 

§  7.  This  foregoing  section  has  been  no  digression,  for  we 
may  consider  both  addition  and  subtraction  as  cases  of  the 
process  we  have  just  sketched.  Let  us  clear  our  ideas  by 
asking  what  we  mean  by  the  simple  proposition  "  Twice  one 
is  two."  Do  we  mean  to  assert  that  one  unit  and  another  unit 
are  the  integer  two  ?  Such  a  statement  would  be  false,  for  the 
integer  is  more  than  one  unit  considered  along  with  another 
unit.  There  is  a  quality  in  the  whole,  which  belongs  to  the 
units  first  when  combined  and  made  into  an  integer.  It  is 
false  then  that  "  one  and  one  are  two."  They  make  two,  but 
do  not  make  it  unless  I  put  them  together  ;  and  I  need  not  do 
so  unless  I  happen  to  choose.  The  result  is  thus  hypothetical 
and  arbitrary. 

§  8.  There  is  a  mistake  we  must  correct  before  we  proceed. 
The  reader  may  (or  may  not)  be  aware,  that  the  logical  and 
temporal  relation  which  exists  between  degree  and  quantity  is 
a  difficult  subject.  It  is  a  question  that  could  not  be  fully 
discussed  in  a  narrow  compass,  and  on  which  we  can  offer  but 
a  brief  observation.  You  may  use  "  degree "  in  more  than 
one  sense.  You  may  understand  by  the  term  a  scale  of 
qualities  which  are  related  explicitly  to  a  scale  of  quantities^ 
and  which  depend  on  this  scale.  Or  again  you  may  mean  a 
scale  of  differences,  which  are  simply  felt  as  more  or  less  of  a 
certain  thing,  but  which  are  not  referred  to  any  scale  of 
numbers  of  units.  If  we  adopt  the  former  sense  of  degree, 
then  both  in  time  and  logically  the  knowledge  of  number,  or 
the  power  of  counting,  precedes  the  knowledge  of  that  scale  of 
intensities  which  stands  in  explicit  relation  to  the  varying 
units.  Quantity  here  will  precede  degree.  But,  if  we  use  the 
latter  meaning  and  understand  by  degree  the  mere  vague 
sense  of  a  more  and  a  less,  of  a  rise  and  a  fall,  a  swelling  and 
a  shrinking,  then  without  any  doubt  degree  comes  first  and 
quantity  follows. 

The  mistake  we  referred  to  springs  partly  from  the  neglect 
of  these  metaphysical  abstractions,  and  partly  from  blindness 
to  palpable  facts.  It  is  assumed,  that  the  perception  of 
differences  in  quantity  implies  the  power  of  counting  units. 


Chap.  II.]  FRESH   SPECIMENS  OF  INFERENCE.  3/1 

There  is  a  well-known  tale,  not  worth  repeating,  of  the 
experiment  which  proves  that  a  magpie  can  count  up  to  two 
or  three,  but  not  any  further.  Thus  if  three  men  go  in  and  but 
two  come  out,  the  bird  knows  that  all  have  not  been  accounted 
for,  and  therefore  it  counts.  But  if  so,  and  if  the  power  to 
perceive  the  difference  of  more  food  and  less  food,  a  larger 
beast  and  a  smaller  beast,  demonstrate  counting,  few  animals 
will  not  count.  If  again  the  ability  to  distinguish  part  from 
the  whole,  and,  when  but  part  appears,  to  expect  the  rest, 
shows  the  practice  of  arithmetic — then  the  higher  animals  are 
all  arithmeticians,  and  all  habitually  add  and  subtract.  This 
perhaps  may  not  seem  a  rediictio  ad  absurdtim,  but  then  this 
is  not  all.  Though  the  higher  (and  even  lower)  animals  can 
all  count,  there  are  races  of  men  who  can  hardly  count  at  all, 
and  are  only  beginning  in  the  rudest  way.  But  these  very 
savages,  who  are  staggered  by  the  difference  between  three 
and  four,  and  are  thus  led  into  errors  which  would  never  occur 
to  an  average  dog — on  the  other  hand  count  much  better  than 
we  could.  Take  one  from  a  flock  of  forty  sheep,  and  in  a 
moment  they  perceive  the  difference.  They  have  finished 
counting  before  we  could  have  begun.  And  on  this  view 
of  the  subject  I  think  it  is  clear  that  there  is  something 
unexplained. 

The  mistake  lies  in  the  failure  to  see  that  number,  in  the 
proper  sense,  is  a  late  product  of  abstraction,  and  that,  long 
before  this  could  come  into  the  world,  the  perception  of  more 
and  less,  of  the  whole  and  the  parts,  already  existed.  They 
existed  in  an  unanalyzed  qualitative  form. 

§  9.  Now  this  observation  has  important  consequences,  for 
it  points  to  the  conclusion  that,  in  considering  number,  we 
have  no  right  to  strike  out  the  qualitative  side.  If  the 
confused  feeling  of  difference  in  degree  between  wholes  came 
first,  and  these  wholes  were  then  afterwards  analyzed  into 
parts,  and  these  parts  were  then  once  again  reduced  to 
equivalent  units — if  this  was  the  psychological  process,  as  I 
think  we  may  agree  it  clearly  must  have  been — then  I  venture 
to  argue  that  this  shows  we  are  wrong,  if  we  take  quantities 
to  consist  in  nothing  but  units,  somehow  taken  together  and 
barely  co-existing.      Even  when   we  get   down   to   abstract 

2  B  2 


372  THE   PRINCIPLES  OF   LOGIC.  [Bk.  IIL  Pt.  L 

number,  each  integer  must  be  more  than  units  and  units.  As 
an  integer  it  will  have  an  additional  quality  which  results 
from  addition  and  disappears  on  subtraction.  One  and  one 
are  not  the  same  as  two,  two  and  two  are  not  the  same  as 
four,  nor  are  they  the  same  as  three  and  one.  For  integers 
are  individuals ;  each  has  an  unity  which  makes  it  a  whole, 
and  joins  together  its  units  by  a  higher  bond  than  mere 
co-existence  before  the  attention.  If  that  bond  is  a  residuum 
of  spatial  perception  or  comes  from  elsewhere,  we  need  not 
here  consider.  Enough  that  it  exists,  that  each  integer  is 
one  whole,  with  qualitative  relations  of  higher  and  lower 
persisting  between  it  and  other  integers.  Hence  we  may  say 
that  mere  counting  is  not  the  integers ;  it  does  but  make 
them.  It  progressively  produces  and  destroys  them  as  it 
goes  up  and  down  the  scale. 

The  integer  then  is  different  from  its  units.  To  say  of 
the  units  that  they  are  the  integer,  is  not  a  tautology  but  a 
downright  false  statement.  That  they  become  the  integer,  on 
the  other  hand  is  true  and  is  not  a  tautology. 

§  lo.  Addition  and  subtraction  produce  new  results ; 
they  are  ideal  operations  which  give  conclusions,  and  justify 
what  they  give ;  they  are  palpable  inferences.  The  reason- 
ing which  they  employ  no  doubt  may  be  very  simple  in  its 
nature  and  very  easy  to  disparage.  "  It  is  the  work  of  a 
machine,"  we  may  hear  the  reproach,  "  and  not  of  a  brain." 
But  if,  starting  from  certain  data,  it  is  a  brain  that  by  means 
of  ideal  experiment  procures  a  fresh  judgment,  we  must  call 
this  reasoning ;  for  we  do  not  know  what  else  we  can  call  it. 
And  the  reproach,  we  must  add,  betrays  a  prejudice  that  is 
not  philosophical. 

The  operation  is  the  analogue  of  that  arbitrary  arrange- 
ment in  ideal  space  which  we  mentioned  above  (§  6).  We 
start  with  the  units  one  and  one,  we  freely  rearrange  them, 
and  we  end  with  the  result  of  integer  two.  But  the  result  is 
hypothetical,  for  we  can  not  say,  one  and  one  must  give  two. 
They  may  be  arranged  in  such  a  way  that  two  must  appear, 
or,  if  I  choose  to  manipulate  one  and  one,  then  two  comes  out. 
Hence  there  is  nothing  categorical.  One  and  one,  if  I  leave 
them  alone,  are  one  and  one.     I  may  handle  them  or  not  at 


Chap.  II.]  FRESH   SPECIMENS  OF  INFERENCE.  3/3 

my  private  pleasure,  and  when  I  handle  them,  I  need  not  add 
them.  They  do  not  necessitate  their  own  addition,  it  is  only 
when  I  add  them  that  necessity  appears.  But  then  they 
must  become  two,  and  I  have  made  an  inference. 

This  is  still  more  patent  if.  we  consider  subtraction.  We 
might  say  "  Three  is  one,"  or  "  The  integer  three  is  one  of  its 
units  ; "  and  of  course  such  a  proposition  would  be  false.  But 
the  integer  turns  of  necessity  to  one  unit,  when  I  first  break 
it  up  and  then  set  aside  two  of  its  component  parts.  Three,  if 
two  be  subtracted,  is  obviously  one  ;  but  this  result  is  hypo- 
thetical. We  are  not  obliged  to  analyze  the  datum  and  to  set 
part  on  one  side  ;  and  we  are  in  no  way  compelled  to  get  the 
conclusion  unless  we  have  taken  this  arbitrary  step. 

§  II.  These  inferences,  it  is  clear,  will  not  come  under  the 
formula  we  set  up.  They  suit  it  no  better  than  did  that  ideal 
arrangement  of  wholes  in  space,  which  gave  a  new  quality. 
But  we  need  not  dwell  on  this  point,  for  there  is  something 
which  presses  for  more  serious  attention.  "The  above 
account,"  it  may  fairly  be  said,  "is  not  a  right  view  of 
addition  and  subtraction,  for  these  give  a  conclusion  which  is 
true  categorically.  Arithmetical  judgments  are  in  no  sense 
arbitrary,  nor,  given  the  data,  is  the  inference  conditional. 
Bricks  and  mortar,  if  the  builder  choose,  may  make  a  house ; 
but  one  and  one  are  equal  to  two,  whether  we  choose  or  do 
not  choose  to  have  it  so."  I  admit  the  distinction  and  desire 
to  endorse  it,  but  it  is  in  no  sense  contrary  to  the  statement 
we  have  made ;  for,  up  to  this  time,  we  have  never  said  a 
word  about  equality.  What  we  wanted  was  to  emphasize  a 
side  of  arithmetical  processes,  which,  if  neglected,  makes  them 
obscure  or  tautologous;  and,  whatever  else  is  right,  it  still 
remains  true  that  addition  is  an  inference  of  the  kind  we 
described.  It  does  prove  hypothetically  that,  if  units  are 
added,  they  become  something  different ;  and  for  the  right 
understanding  of  the  subject  this  truth  is  all  important. 

Having  made  this  clear,  we  may  now  proceed  to  regard 
the  process  from  a  different  side,  and  to  consider  it  as  a 
categorical  proof  of  equality  in  difference. 

§  1 2.  What  is  equality  }  It  is  certainly  not  the  same  as 
mere   identity,  nor  would  it  be  safe  for  any  one   except  a 


374  THE   PRINCIPLES  OF   LOGIC.  [Bk.  III.  Pt.  I. 

"  powerful  thinker  "  to  be  guilty  of  such  elementary  confusion. 
Because  things  are  the  same  they  need  not  be  equal  ;  and 
when  they  are  equal,  they  need  not  be  the  same  in  more  than 
one  aspect.  Equality  is  sameness  in  respect  of  quantity,  it  is 
a  relation  between  things  that  may  otherwise  be  different,  but 
are  identical  in  regard  to  their  number  of  units.  Or,  more 
accurately,  we  may  call  it  the  identity  of  the  units,  as  units,  in 
two  different  things.  This  definition  certainly  gives  rise  to 
problems  which  in  another  place  I  should  be  glad  to  discuss  ; 
but  for  present  purposes  it  will  be  found  sufficient.  One  and 
one  are  equal  to  two  because  the  mere  units  in  both  are  the 
same,  and  three  minus  two  is  equal  to  one  because  on  both 
sides  the  unit  is  identical. 

This  result  is  true,  and  it  seems  categorical,  and  we 
therefore  are  led  to  ask  once  more  how  we  reach  the  result. 
If  the  conclusion  is  not  hypothetical,  were  we  right  in  taking 
the  operation  to  be  arbitrary }  Yet,  on  the  other  hand,  how 
do  I  know  that  one  and  one  are  equal  to  tv/o  }  I  know  it 
because  when  I  add  the  units,  they  become  two,  and  when  I 
analyze  two  it  becomes  the  units.  I  thus  see  the  identity  of 
the  units  throughout,  but- 1  see  it  in  consequence  of  a  free 
manipulation  which  I  might  have  omitted.  So  again  in 
subtraction  I  infer  that  3  —  2=1.  But  how  do  I  reach  this? 
I  break  up  the  three  into  three  separate  units  ;  I  break  up  the 
two  in  the  selfsame  manner,  and,  removing  it,  I  perceive  that 
two  units  of  the  three  h^ve  been  removed.  One  is  left,  and 
that  as  an  unit  is  precisely  the  same  as  any  other  one.  The 
conclusion  is  necessary,  but  the  operation  is  optional,  for 
there  was  nothing  which  demanded  my  analysis  and  compari- 
son.    The  result  has  thus  depended  on  my  arbitrary  choice. 

§  13.  We  seem  left  with  this  difficulty — the  result  is 
unconditional,  though  the  process  on  which  it  depends  is 
arbitrary.  And  this  difficulty  for  the  present  must  be  simply 
accepted.  We  are  indeed-  only  too  ready  to  accept  it  or 
ignore  it.  The  operation  in  arithmetic,  which  gives  the  result, 
is  supposed  to  have  no  influence  upon  it  ;  there  is  a  postulate 
that,  so  long  as  you  do  not  alter  the  number  of  the  units,  you 
may  do  what  you  please  with  them,  and  whatever  you  bring 
out  is  unconditionally  true.     The  process  is  a  mere  prepar^i- 


CuAP.  II.]  FRESH   SPECIMENS   OF   INFERENCE.  375 

tion  of  the  data,  and  it  demonstrates  an  element  which  already 
was  there.  It  is  not  an  arbitrary  alteration  of  my  own,  since 
it  does  not  alter  the  element  at  all  ;  it  constructs  no  artificial 
and  novel  spectacle,  it  does  but  remove  an  obstacle  to  my 
vision. 

In  other  words  the  relation  of  equality  between  any 
quantities  is  supposed  to  exist,  and  the  judgment  which 
expresses  it  is  supposed  to  have  independent  validity. 
Whether  I  see  it  or  not,  it  is  taken  to  be  true,  and  the  way  in 
which  I  get  to  it  affects  it  in  no  way.  Thus  my  inferring  is 
optional  and  entirely  arbitrary — but  the  inference  itself  is 
eternal  truth.  It  is  my  process  from  a  datum  which  enables 
me  to  see  what  is  true  of  that  datum,  yet  it  is  only  my  insight, 
and  it  is  not  the  truth,  which  depends  on  that  process.  One 
and  one  =  two,  not  because  I  add  them,  but  because  they  are 
equal. 

§  14.  The  general  relation  of  the  ground  of  knowledge  to 
the  ground  of  reality  will  vex  us  hereafter,  and  we  will  not 
anticipate  ;  for  our  present  task  is  simply  to  find  the  process 
which  is  used.  It  consists,  as  we  have  seen,  in  a  free  re- 
arrangement, resulting  in  a  perception  of  quantitative  identity, 
which  is  taken  as  true  independent  of  the  process.  The  new 
result,  which  is  got  by  experiment  with  the  units,  is  held  valid 
of  those  units  apart  from  the  experiment.  And  we  do  not 
propose  in  the  present  chapter  to  question  this  result ;  but,  the 
process  being  such,  our  wish  is  to  know  if  it  really  is  an 
inference,  and  again  if  it  will  come  under  the  formula  which 
we  first  accepted  but  now  hold  suspect. 

That  it  really  is  inference  we  can  not  long  doubt.  We 
might  indeed  dispute  for  ever  about  "  twice  one  is  two  ; "  for, 
when  a  product  has  been  learnt  before  it  was  understood,  and 
now  comes  to  the  mind  as  so  ready-made,  self- apparent,  and 
obvious,  it  is  hard  to  see  that  it  ever  has  been  a  painful 
inference,  a  slow  result  of  time  for  which  ages  had  to  wait. 
But  more  complex  instances  soon  convict  us  of  our  error. 
The  moment  we  desert  the  table  we  have  learnt,  we  find  there 
is  a  process  which  proves  the  result,  and  in  which  mistakes 
are  only  too  easy.  And  this  process  is  the  movement  of  an 
ide^l  experiment  which  gives    a  judgment  we  had  not  got 


376  THE   PRINCIPLES  OF  LOGIC.  [Bk.  III.  Pt.  1. 

before.  But,  unless  we  have  somehow  apart  from  the  facts 
decided  in  our  minds  what  reasoning  is  to  be,  then  this  must 
be  reasoning  and  its  result  must  be  an  inference. 

But  is  it  an  inference  according  to  our  formula  ?  That  at 
least  it  can  not  be,  for  it  establishes  no  relation  between  the 
terms  of  the  premises.  On  the  contrary  the  relation,  which 
appears  in  the  conclusion,  has  one  terminal  point  which  never 
appeared  in  the  data  at  all.  Our  poor  formula  at  this  rate 
will  hardly  be  able  to  claim  respectful  treatment  in  the  future, 
and  what  presumption  there  is  seems  against  its  virtue. 

§  15.  Spaces  and  times  admit  of  treatment  by  a  similar 
process.  If  an  optional  arrangement  of  superposition,  division 
into  parts,  or  construction  into  a  whole  by  arbitrary  additions, 
results  in  relations  of  equality  or  inequality,  this  result  is  taken 
as  a  categorical  conclusion.  The  alterations  which  we  in- 
troduce do  not  alter  the  fact  as  long  as  they  do  not  alter  the 
magnitude  ;  and  it  is  a  postulate  that  no  change  of  place  or 
context,  no  analysis  or  synthesis,  can  make  any  difference  to 
the  relations  of  quantity.  The  operations  (we  assume)  are 
external  to  the  data  themselves ;  the  work  done  upon  them  is 
really  work  that  falls  outside  them,  and  that  but  renders  them 
apparent  as  they  were  before.  The  truth  is  shown  to  us  by 
a  process  which  does  not  give  the  reason  why  the  thing 
actually  is  so.  The  demonstration  removes  a  barrier  from  our 
sight,  or  provides  us  with  artificial  vision,  but  it  does  not  pro- 
duce the  fact  from  its  elements. 

Yet  we  can  not  doubt  that  here  once  more  we  have  an 
inference  ;  an  inference  again  which  we  have  failed  to  provide 
for,  since  it  can  not  be  reduced  to  interrelation.  When  I  show, 
for  instance,  by  superposition  that  one  triangle  is  equal  to 
another,  what  third  term  is  it  that  connects  the  couple,  or 
what  syllogism  will  express  the  actual  process  }  I  know  that 
an  application  of  reckless  torture  will  reduce  anything  you 
please  to  any  possible  form  ;  but  the  fact  remains  otherwise. 
We  have  here  an  intuition  of  comparison,  taking  place  by 
means  of  free  ideal  rearrangement.  This  is  an  inference, 
and  it  is  a  new  kind  of  inference. 

§  16.  (C)  And  new  itself  it  suggests  fresh  innovation,  for 
it  leads  us  to  ask  if  comparison  is  reasoning,  and  if,  whenever 


Chap.  IL]  FRESH   SPECIMENS   OF   INFERENCE.  37/ 

we  compare,  we  may  be  said  to  infer.  The  suggestion  is 
contrary  to  our  established  ideas,  but  how  can  we  repulse  it .? 
We  start  from  data,  we  subject  these  data  to  an  ideal  process, 
and  we  get  a  new  truth  about  these  data.  The  new  truth,  so 
far  as  our  knowing  it  is  concerned,  depends  on  the  operation, 
is  because  of  it,  and  would  not  be  unless  for  that  reason  ; 
but  if  so,  we  surely  must  call  it  a  conclusion. 

Take  an  instance  ;  we  have  ABC,  DBF,  and  we  may 
not  know  that  they  are  the  same  in  any  point.  We  then 
inspect  them  with  a  desire  to  discover  sameness,  general  or 
special ;  that  is  we  attend  to  them  from  a  certain  point  of 
view.  We  compare  them  in  respect  of  identity,  either  in 
quality  or  quantity  or  again  in  some  more  special  develope- 
ment.  No  doubt  it  is  not  easy  to  lay  down  the  precise 
character  of  the  process  employed,  but  there  certainly  is  some 
process.  There  is  an  ideal  operation  on  ABC,  DBF,  and 
that  operation  presents  us  with  a  judgment.  We  did  not 
know  that  ABC,  DBF  were  alike,  now  we  know  that 
they  possess  the  point  B  in  common,  and  this  intuition  depends 
on  the  operation.  The  conclusion  runs  "  If  ABC,  DBF  are 
compared  they  are  alike  in  B  ; "  and,  since  the  operation  is 
assumed  to  make  no  difference  to  the  fact,  we  may  say 
categorically,  "  The  two  are  alike."  No  doubt  we  may  question 
the  validity  of  this  inference,  but  I  do  not  see  how  we  can 
deny  its  existence.  On  the  other  hand  it  is  not  a  relation 
between  two  given  terms  that  is  seen  in  a  construction  through 
identity. 

We  shall  perhaps  not  be  wrong  to  place  under  this  head 
the  copulative  process  "  A  is  C,  B  is  C,  and  therefore  both  are 
C."  So  far  as  this  connects,  and  does  not  barely  conjoin,  it 
concludes  to  an  identity  between  A  and  B. 

§  17.  And  what  holds  of  the  comparison  which  establishes 
identity,  must  hold  too  of  the  process  which  brings  out  differ- 
ence. If  distinction  is  an  ideal  operation  which  demonstrates 
new  truth,  that  is  truth  new  to  us,  then  so  far  it  must  be 
reasoning.  We  may  illustrate  simply  ;  what  is  really  B^B^B^ 
has  been  taken  throughout  as  simply  B.  We  subject  this 
datum  B  to  an  ideal  process,  the  nature  of  which  we  do  not 
at  present  discuss,  and  the  result  is  B^B^B^.     Now  since  the 


378  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  L 

Operation  is  arbitrary  the  product  is  hypothetical,  but  be- 
cause once  again  the  operation  is  assumed  not  to  alter  the 
dattciHy  as  it  really  is — we  take  the  product  as  categorical. 
The  marks  have  been  found,  and  therefore  they  are.  True 
there  is  no  distinction  unless  things  are  first  different ;  but 
for  us  there  can  be  no.  difference  which  does  not  follow  on 
distinction.  It  becomes  apparent  and  is  shown  to  exist  by 
virtue  of  a  process,  which  must  therefore  be  taken  as  a  de- 
monstration and  a  genuine  inference. 

A  difficulty,  we  admit,  besets  the  operations  of  distinction 
and  identification  ;  for  they  do  not,  it  may  be  said,  give  the 
actual  reason  of  the  real  truth  in  which  we  are  finally  landed. 
Nay  they  do  not  even  profess  to  give  it,  and  we  may  say  that 
they  even  protest  above  all  things  that  they  demonstrate  nothing 
that  was  not  there  without  them.  This  difficulty,  which  has 
bearings  we  perhaps  do  not  suspect,  will  engage  us  hereafter. 
But  for  our  present  purpose  we  must  insist  on  the  other  side  of 
the  process.  We  have  reached  a  result  by  ideal  experiment ; 
and  of  this  we  can  say.  Though  it  be  not  made  true  by  our 
operation,  yet  we  know  it  for  that  reason,  and  it  is  for  us 
because  of  our  activity.  But,  if  so,  then  once  again  we  have 
reasoned. 

§  1 8.  (D)  Jt  would  seem  that  we  may  reason,  though  we 
do  not  give  the  reason  of  the  fact  itself,  and  when  our  demon- 
stration less  establishes  than  recognizes.  Mere  consistency 
now  prompts  us  to  raise  the  doubt  if  recogitition  is  not  always 
reasoning.  And  perhaps  to  our  surprise  we  discover  that  this 
is  really  the  case,  for  to  find  that  AB  is  C,  and  to  recognize 
it  as  such,  implies  a  process  of  ideal  redintegration.  I  start 
with  AB,  and  the  function  of  ideal  synthesis  BC  supplies  the 
construction  from  which  I  proceed.  Even  where  I  merely 
recall  the  name,  or  where  I  can  but  say  that  somewhere  I 
must  have  seen  that  face  before,  there  is  still  a  conclusion. 
The  connection  may  be  dim  and  the  element  that  is  added 
may  be  trifling  or  obscure  ;  but  whatever  it  is,  we  get  it  by  a 
synthetic  process  of  restoration,  and  this  is  reasoning. 

"  Yes,  reasoning,"  I  may  be  told,  "  but  normal  reasoning  and 
with  the  usual  three  terms.  First  AB  and  BC,  then  a  whole 
ABC,    and    an    elision    leaving   the    result    A  —  C."     But,    I 


Chap.  II.]  FRESH   SPECIMENS  OF   INFERENCE*.  379 

answer,  in  what  sense  is  BC  a  premise  ?  It  is  by  no  means 
an  original  datum.  Indeed  it  is  not  a  datum  at  all ;  for  it  is 
a  function  which  does  not  come  before  the  mind,  but  which 
presents  the  result  of  its  action  on  the  only  datum  that  we 
possess.  If  BC  is  a  premise,  it  is  a  premise  in  no  usual 
sense  of  the  term.  We  have  at  any  rate  found  a  case  that 
has  not  been  yet  provided  for,  and  a  case  where  the  inference 
seems  quite  indisputable. 

We  may  add  to  this  section  a  remark  on  the  hypothetical 
judgment.  This  is  always  an  inference.  I  do  not  simply 
mean  that  it  is  an  inference,  when  we  first  say,  "  If  anything 
is  B  it  is  C,  but  here  A  is  B,  and  therefore  it  is  C."  The 
inference  I  mean  is  one  which  dispenses  with  the  explicit 
statement  of  the  general  principle.  A  is  merely  supposed  ; 
it  is  offered  in  experiment  as  an  attribute  of  reality,  and  from 
this  we  go  on  to  arrive  at  C  without  any  other  premise 
which  comes  before  the  mind.  This  process  is,  I  think,  an 
inference  of  a  kind  we  did  not  anticipate  ;  but  it  hardly  can 
claim  an  independent  position.  Where  it  does  not  fall  under 
the  foregoing  head  of  Recognition,  it  will  find  its  place  in 
the  ensuing  section. 

§  19.  (E)  The  subject  of  this  section  is  forced  upon  us. 
I  should  be  very  glad  in  a  work  of  this  kind  to  say  nothing 
about  the  Dialectic  Method,  but  I  can  find  no  excuse  for 
passing  it  over,  for  it  is  irresistibly  suggested  by  the  inference 
which  we  had  to  notice  last.  I  am  far  from  implying  that  the 
Method  falls  under  the  previous  section,  and  that  it  is  a 
mere  process  of  recognition.  Such  a  view,  if  adopted,  would 
annihilate  its  claims,  and  my  object  is  here  not  to  criticize  or 
to  advocate*  I  wish  simply  to  consider  what  sort  of  operation 
is  performed  by  Dialectic,  assuming  that  it  has  a  real  way  of 
its  own. 

If  we  make  that  assumption,  we  pass  naturally  from  the 
process  of  Recognition  on  to  the  Dialectic  movement.  Like 
recognition  this  starts  from  a  single  datum,  and  without  the 
help  of  any  other  premise  it  brings  out  a  fresh  result.  Yet 
the  result  is  not  got  by  mere  analysis  of  the  starting-point, 
but  is  got  by  the  action  of  a  mental  function  which  extends 
the  datum  through  an  ideal  synthesis.     So  far  the  rnethod  of 


380  THE   PRINCIPLES   OF  LOGIC.  [Bk.  IIL  Pt.  L 

Dialectic  is  precisely^  the  same  as  the  common  recognition 
which  works  by  means  of  redintegration.  But  now  comes  a 
difference ;  the  ideal  synthesis,  which  in  Dialectic  meets  and 
supplements  the  starting-point,  is  not  reproduction  from  past 
perception ;  or  rather,  and  to  speak  more  correctly,  it  is  not 
merely  such  ideal  reproduction.  Even  though  the  synthesis 
which  it  brings  into  play  does  repeat  a  connection  we  have 
got  from  presentation,  there  still  is  more  than  bare  repetition. 
The  function  is  felt  not  as  what  the  mind  does  because  it  has 
thus  been  trained  to  perform  :  the  naturalness  seems  more  than 
the  ease  of  habit,  and  the  necessity  above  any  vis  inertice. 
And  the  cause  of  the  difference  we  find  is  this  ;  the  message 
in  the  one  case  seems  external  tidings  which  are  so  believed, 
since  thus  received ;  but  in  the  other  it  seems  like  a  reve- 
lation of  ourselves,  which  is  true  because  we  have  the  witness 
in  our  own  experience.  The  content  in  one  case,  itself 
irrational,  seems  to  come  to  our  reason  from  a  world  without, 
while  in  the  other  it  appears  as  that  natural  outcome  of  our 
inmost  constitution,  which  satisfies  us  because  it  is  our  own 
selves.  This  internal  necessity,  of  the  function  and  of  its 
product,  is  the  characteristic  of  the  Dialectical  Method  and 
constitutes  its  claim  and  title  to  existence. 

§  20.  I  do  not  propose  to  criticize  that  title,  and  prefer  to 
attempt  the  removal  of  misunderstandings.  One  of  these  we 
have  already  noticed ;  you  make  no  answer  to  the  claim  of 
Dialectic,  if  you  establish  the  fact  that  external  experience 
has  already  given  it  what  it  professes  to  evolve,  and  that  no 
synthesis  comes  out  but  what  before  has  gone  in.  All  this 
may  be  admitted,  for  the  question  at  issue  is  not,  What  can 
appear  and  How  comes  it  to  appear  1  The  question  is  as  to 
the  manner  of  its  appearing,  when  it  is  induced  to  appear,  and 
as  to  the  special  mode  in  which  the  mind  recasts  and  regards 
the  matter  it  may  have  otherwise  acquired.  To  use  two 
technical  terms  which  I  confess  I  regard  with  some  aversion — 
the  point  in  dispute  is  not  whether  the  product  is  a  posteriori^ 
but  whether,  being  a  posteriori^  it  is  not  a  priori  also  and  as 
well.  And  misunderstanding  on  this  head  has  caused  some 
waste  of  time. 

The  second  misunderstanding  is  of  a  different  nature.     An 


CiiAP.  n.]  FRESH   SPECIMENS  OF   INFERENCE.  38 1 

idea  prevails  that  the  Dialectic  Method  is  a  sort  of  experi- 
ment with  conceptions  in  vaato.  We  are  supposed  to  have 
nothing  but  one  single  isolated  abstract  idea,  and  this  solitary 
monad  then  proceeds  to  multiply  by  gemmation  from  or  by 
fission  of  its  private  substance,  or  by  fetching  matter  from  the 
impalpable  void.  But  this  is  a  mere  caricature,  and  it  conies 
from  confusion  between  that  which  the  mind  has  got  before  it 
and  that  which  it  has'within  itself.  Before  the  mind  there  is 
a  single  conception,  but  the  whole  mind  itself,  which  does  not 
appear,  engages  in  the  process,  operates  on  the  datum,  and 
produces  the  result.  The  opposition  between  the  real,  in 
that  fragmentary  character  in  which  the  mind  possesses  it,  and 
the  true  reality  felt  within  the  mind,  is  the  moving  cause  of 
that  unrest  which  sets  up  the  dialectical  process. 

§  21.  We  may  understand  that  process  in  two  different 
ways.  On  one  view  the  method  advances  on  the  strength  of 
negation  ;  the  synthesis,  which  unites  and  adds  a  fresh  ele- 
ment, comes  always  from  denial,  and  from  the  conti^adiction 
of  the  starting-point.  Every  truth  is  taken  to  have  two  sides, 
and  to  consist  in  the  assertion  of  a  pair  of  correlatives,  each  of 
which  is  the  logical  negation  of  the  other.  Each  of  these  by 
consequence,  to  assert  itself,  denies  the  other  ;  but  at  the 
same  time  each  depends  on  what  it  denies,  and  so  reasserts  it. 
Affirming  itself,  it  thus  on  the  other  hand  is  driven  to  affirm 
its  own  negation,  and  so  becomes  its  own  opposite  by  a  self- 
seeking  self-denial.  Or,  more  correctly,  the  whole,  which  is 
both  sides  of  this  process,  rejects  the  claim  of  a  one-sided 
datum,  and  supplements  it  by  that  other  and  opposite  side 
which  really  is  implied — so  begetting  by  negation  a  balanced 
unity.  This  path  once  entered  on,  the  process  starts  afresh 
with  the  whole  just  reached.  But  this  also  is  seen  to  be  the 
one-sided  expression  of  a  higher  synthesis  ;  and  it  gives  birth 
to  an  opposite  which  co-unites  with  it  into  a  second  whole,  a 
whole  which  in  its  turn  is  degraded  into  a  fragment  of  truth. 
So  the  process  goes  on  till  the  mind,  therein  implicit,  finds  a 
product  which  answers  its  unconscious  idea  ;  and  here,  having 
become  in  its  own  entirety  a  datum  to  itself,  it  rests  in  the 
activity  which  is  self-conscious  in  its  object.  This  great  ideal 
of  self-developement  and    natural    evolution    led    in    Hegel's 


382  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

hands  to  most  fruitful  results,  and  in  the  main  these  will 
stand  when  the  principle  of  negativity  is  rejected  as  an  error. 

For  the  Dialectic  Method  does  not  necessarily  involve  the 
identity  of  opposites,  in  the  sense  that  one  element  in  its  own 
assertion  supplements  itself  by  self-denial  ;  and  it  is  possible 
to  take  a  simpler  view  which  keeps  clear  of  this  difficulty. 
We  may- suppose,  as  before,  that  the  reality  has  before  it  and 
contemplates  itself  in  an  isolated  datum.  What  comes  next 
is  ±hat  the  datum  is  felt  insufficient,  ajid  as  such  is  denied. 
But  in  and  through  this  denial  the  reality  produces  that 
supplement  which  was  required  to  complete  the  datum^  and 
which  very  supplement,  forefelt  in  the  mind,  was  the  active 
base  of  the  dissatisfaction  and  the  consequent  negation.  The 
important  point  is  that,  on  this  second  view,  both  sides  of  the 
correlation  are  positive,  and  one  is  not  the  mere  denial  of 
the  other.  The  presence  of  either  is  inconsistent  with  the 
absence  of  the  other,  and  it  is  inconsistent  with  the  solitary 
presence  of  the  other.  Thus  either  by  itself  is  denied,  not  by^ 
but  from  the  ground  of  its  positive  counterpart,  which  in  that 
denial  makes  itself  conscious  and  so  comes  to  light.  I  am 
perfectly  aware  that  this  doctrine  is  a  heresy ;  but  it  is  a 
heresy  which,  I  think,  will  be  found  to  save  the  real  substance 
of  the  orthodox  doctrine. 

§  22.  We  are  not  concerned  here  with  the  truth  of  this 
heresy,  and  we  turn  to  the  question  which  is  really  in  hand  ;  In 
what  sense  is  Dialectic  an  inference  }  It  certainly  is  reason- 
ing, which  by  an  ideal  operation  gets  a  fresh  result.  Take  a 
datum  a,  and  by  your  operation  you  get  a  —  yS  with  a  further 
result  7.  The  conclusion  here  is,  that  a  musf'be  /S,  and  there- 
fore it  is  7.  And  because  the  operation  is  not  arbitrary,  because 
throughout  it  keeps  to  reality,  you  have  no  hypothesis.  For 
your  middle  is  not  something  you  have  chosen  to  make ;  it  is 
wholly  necessary,  and  hence  you  may  end  in  the  conclusion, 
a  is  7.  We  need  hardly  ask  if  our  original  formula 
provided  for  this  inference. 

§  23.  (F)  We  next  may  take  the  process  of  abstraction. 
In  recognition  we  used  a  function  of  synthesis  which  was 
clearly  universal,  and  it  is  natural  to  ask  how  this  function  is 
acquired.     If  it   comes  from   an   operation   of  analysis   and 


Chap.  IL]  FRESH  SPECIMENS  OF  INFERENCE.  383 

abstraction,  we  are  thence  led  to  ask  whether  such  an  opera- 
tion must  not  be  an  inference.  For  it  is  an  ideal  experiment 
which  procures  a  new  result.  We  start  here  with  a  given 
whole  abed ;  we  operate  on  this  by  the  neglect  of  or  by  the 
removal  of  bc^  and  ad  is  left ;  and  we  then  predicate  this  ad  of 
the  reality.  The  real  was  abed,  and  in  consequence  of  our 
action  we  know  now  it  is  ad.  The  nature  of  the  process  by 
which  we  remove  what  seems  unessential,  need  not  at  present 
be  discussed,  but  it  is  certain  that  there  is  some  process,  and 
that  the  result  of  this  process  is  accepted  as  truth  for  no  other 
reason.  And  once  again  it  is  true  that  the  experiment  is 
arbitrary,  for  we  need  not  perform  it,  and  it  is  not  supposed  to 
make  a  difference  to  the  fact  itself.  Still  it  makes  a  difference 
to  our  knowledge  and  judgment,  it  supplies  the  because  of  a 
new  perception,  and  it  has  therefore  the  mark  of  reasoning 
and  inference. 

§  24.  We  have  first  analysis,  then  elimination  or  elision  of 
part  of  the  content,  followed  in  the  end  by  a  positive  attri-. 
bution  of  the  remaining  content  to  the  original  subject.  The 
operation  is  familiar  and  is  largely  employed,  but  its  validity 
is  open  to  grave  objection.  We  shall  consider  this  hereafter, 
but  may  remark  at  present  that  the  doubt  is  whether  by  your 
elimination  you  have  not  fatally  altered  the  subject.  By 
removing  one  element  you  may  destroy  the  condition  which 
made  the  rest  predicable.  Our  old  friend,  J.  S.  Mill's  so- 
called  Method  of  Difference,  fell  into  this  blunder,  and  may 
serve  us  as  a  warning  (Book  II.  Part  II.  Chap.  III.).  Reality 
was  first  ABC -^^,  then  BC-^,  and  we  assumed  that,  if  we 
elided  BC  — ^,  we  should  leave  A  — ^  standing  good  of  reality. 
But  here  (we  may  repeat)  were  two  errors.  Suppose  first  that 
our  data  are  pure  universals,  still  you  have  not  experimented 
with  that  very  BC  which  goes  with  A.  You  have  worked 
with  a  second  and  an  other  BC,  and  you  can  not  be  sure  that 
there  is  not  a  difference  in  the  way  in  which  they  operate. 
The  first  BC  may  give  something  to  A,  and  get  something  in 
exchange,  so  that  A  may  be  concerned  in  the  first  ef,  and  BC 
be  partly  concerned  in  d.  This  unconsidered  possibility 
wrecks  your  proof;  and  your  Method  of  Difference  is  self- 
condemned,  since  it  is  not  a  method  of  the  only  difference. 


3^4  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  L 

And  your  error  is  not  single ;  for  you  have  withal  ignored 
the  fundamental  difficulty.  How  can  you  procure  your  pure 
universal  ABC  — def  without  using  to  get  it  a  process  of 
elision,  a  "  method  of  difference,"  which  is  still  more  pre- 
carious .-*  Your  premises,  "Reality  is  KEC  —  def  and  BC 
—  ef"  are  the  products  of  an  abstraction  which  has  separated 
these  elements  from  a  mass  of  detail  in  which  they  appeared. 
This  original  process,  what  justifies  that  ?  What  tells  you 
that  the  detail,  which  you  cut  away,  is  wholly  irrelevant,  and 
that,  without  it,  the  reality  is  still  just  as  much  ABC  — ^^  and 
BC— ^as  it  was  before.?  This  objection  is  as  fatal  to  the 
foundation  of  the'  Method  as  the  former  was  to  its  super- 
structure. It  points  to  the  result  that  a  product  of  elision  is 
always  to  be  received  with  the  gravest  suspicion  ;  and  with 
this  result  we  must  at  present  be  satisfied. 

But,  valid  or  invalid,  abstraction  is  reasoning ;  and  it  does 
not  appear  to  come  under  the  head  of  any  foregoing  process. 

§  25.  (G)  We  have  not  yet  reached  the  end.  In  the 
account,  which  in  our  First  Book  we  gave  of  the  Disjunctive 
judgment,  we  observed  that  it  contained  a  latent  inference  ; 
and  the  time  has  now  come  to  draw  this  to  the  light.  We 
might  indeed  be  tempted  to  dispose  of  the  enquiry  by 
reducing  the  process  to  a  three-term  inference.  "  A  is  <^  or  c, 
A  is  not  c,  and  therefore  it  is  3  " — the  reasoning  here,  we  might 
say,  is  syllogistic,  and  falls  under  the  type,  "  A  not-^  is  i?, 
A  is  A  not-^,  and  therefore  A  is  /^."  But  this  attempt  would 
be  futile,  since  the  reduction  presupposes  that  the  alternatives 
are  stated  explicitly,  in  the  character  of  exclusive  alternatives. 
But  the  question  as  to  how  we  become  possessed  of  this 
explicit  statement,  remains  thus  unanswered,  and  we  shall  find 
that  it  comes  to  us  by  way  of  an  inference  that  is  not 
syllogistic.  The  syllogism  is  not  the  soul  and  principle  of 
disjunctive  reasoning  ;  it  is  an  artificial  way  of  expressing  the 
product  and  result  of  that  reasoning  (Chap.  IV.  §§  6,  7). 

§  26.  Before  it  in  time  and  before  it  in  idea  comes  the 
actual  process,  and  we  must  see  what  this  is.  We  know  that 
A  may  be  d,  and  again  may  be  c,  and  once  more  may  be  d  ; 
we  know  that  it  is  nothing  which  excludes  all  three ;  and  we 
may  call  this  our  starting-point.     We  then  go  on  to  learn  that 


Chap.  II.]  FRESH   SPECIMENS  OF  INFERENCE.  385 

A  is  not  by  and  we  conclude,  that  therefore  it  falls  within  cd. 
Once  more  we  find  that  A  is  not  c^  and  on  this  we  conclude, 
therefore  A  is  d.  We  have  here  an  obvious  and  palpable 
inference,  but  in  what  does  it  consist  ?  It  consists  in  removing 
the  possible  predicates  of  a  given  subject  until  the  residue  is 
self-consistent,  and  in  then  passing  at  once  from  this  residual 
possibility  to  an  assertion  of  its  reality.  One  possibility  is  left, 
and  therefore  that  is  fact 

Our  inference  is  not  got  by  arguing  from  the  major  "  What 
is  not  b  or  c  must  be  d''  and  that  major  does  not  give  the  proof 
of  our  conclusion.  On  the  contrary  our  process  is  the  ideal  ex- 
periment which  proves  this  major.  We  know  that  A,  which 
is  not  b  and  not  c,  must  be  d,  only  because  we  have  tried  and 
have  seen  that  d  comes  out  as  the  result.  Thus  our  major,  if 
we  had  one,  would  be  the  principle  that  a  sole  possibility  must 
be  actual  fact.  But  then  this  again  is  not  given  as  a  premise, 
and  we  do  not  argue  because  we  know  that  this  is  true.  We 
know  it  is  true  because  we  have  argued,  and  itself  is  the  result 
of  ideal  experiment. 

§  27.  And  even  this  principle  is  not  quite  fundamental. 
For  it  presupposes  a  judgment  that  we  have  before  us  an 
explicit  exhaustion  of  the  possibilities  of  A.  One  step  of  our 
reasoning  consisted  in  the  statement,  that  b,  c,  and  d  are  the 
whole  sphere  of  A,  and  that  A  must  fall  (if  anywhere)  within 
this  sphere.  But  the  earliest  form  of  disjunctive  reasoning 
dispenses  with  such  a  preliminary  statement.  Incompatible 
suggestions  with  respect  to  A  come  before  the  mind,  and  the 
suggestion  which  survives  in  that  ideal  struggle  is  accepted 
as  fact.  Thus  we  go  direct  to  the  assertion  without  any 
declaration  that  our  previous  denial  has  exhausted  the  subject 
We  shall  return  to  this  process  when  we  begin  to  sketch  the 
beginnings  of  inference  in  the  lower  stages  of  mind,  and  at 
present  we  must  content  ourselves  with  saying  a  few  words  on 
the  principle  which  underlies  this  early  operation. 

There  is  atr-^ixiom  which  we  cannot  fail  to  use,  how- 
ever little  we  may  be  aware  of  its  nature  or  existence. 
All  suggested  ideas,  we  assume,  are  real,  unless  they  are 
excluded.  If  an  ideal  content  is  disparate  with  reality,  then  it 
is  not  fact     If  again  it  is  disparate  with  another  content,  then 

2  C 


1 


386  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

both  are,  at  present,  not  yet  real.  The  suggested  idea  is 
so  far  possible ;  but  if  nothing  is  found  incompatible  with  it, 
the  idea  is  held  actual.  Thus  all  suggestions  are  true  unless 
they  are  opposed,  and  the  suggestion,  which  maintains  itself 
in  ideal  experiment,  and  abolishes  incompatible  ideas,  has 
demonstrated  its  own  validity.  The  survivor  from  the  struggle 
of  competing  ideas  has  shown  itself  fittest,  and  it  therefore  is 
the  truth.  This  ominous  dictum,  which  contains  the  soul  of 
disjunctive  reasoning,  awakens  our  scruples,  and  when  we 
discuss  the  validity  of  the  process  it  gives  rise  to,  we  shall 
have  to  weigh  these  scruples  in  the  balance.  In  this  place  it 
is  enough  to  have  shown  that  once  more  we  have  found  an 
operation,  which  is  not  three-term  reasoning,  and  which  yet 
lays  claim  to  the  title  of  inference. 

§  28.  It  is  worth  our  while  to  pause  for  a  moment,  and  to  see 
the  extent  over  which  this  principle  operates.  Any  judgment 
whatever  may  be  turned  into  reasoning  by  a  simple  change. 
For  we  have  merely  to  suggest  the  idea  of  the  opposite — we 
have  only  to  suppose  that  the  truth  is  otherwise,  and  at  once 
the  predicate,  which  we  already  possess,  excludes  that  sugges- 
tion and  returns  to  itself  as  what  must  be  true.  It  now  is  real 
because  it  must  be  so  ;  and  it  is  a  necessary  truth,  for  it  has 
entered  the  field  of  ideal  experiment  and  has  returned 
victorious.  The  process  seems  frivolous,  since  it  turns  in  a 
circle  ;  we  return  to  the  place  from  which  we  set  out,  and 
the  predicate  of  necessity  but  adds  the  idle  form  of  "  It  is 
because  it  is  "  (cf  Book  I.  Chap.  V.  §  29).  We  first  degrade 
our  judgment  to  a  mere  idea,  and  then  assert  the  idea  on  the 
strength  of  the  judgment.  But  this  process,  circular  when  we 
apply  it  to  judgments,  is  very  different  when  used  on  mere 
ideas.  Take  any  idea,  no  matter  what  it  is,  suggest  it  of  the 
real  and  find  it  compatible  ;  bring  it  into  collision  with  the 
other  ideas  which  are  disparate  with  itself,  see  that  it  defeats 
them  in  open  competition,  and  then  go  on  at  once  to  assert  its 
truth — this  alarming  process  appears  to  have  no  limit.  Yet 
valid  or  invalid,  it  certainly  is  inference.  Whether  we 
explicitly  state  the  possibilities  as  exhausted,  or  simply  ignore 
their  possible  enlargement,  we  have  in  both  cases  reasoning  of 
a  type  that  does  not  fall  under  any  other  head. 


Chap.  H.]  FRESH   SPECIMENS  OF  INFERENCE.  387 

§  29.  We  may  add  the  remark  that  apagogic  inferences 
belong  to  this  class,  for,  whatever  intermediate  steps  they  may 
employ,  they  in  the  end  must  turn  on  a  disjunction.  They 
make  a  transition  from  the  denial  of  one  predicate  to  the 
assertion  of  another.  And  that  transition  assumes  that  no 
other  possible  predicate  exists.  The  large  amount  of  vicious 
reasoning  which  attends  the  use  of  the  indirect  method,  is 
mainly  due  to  forgetfulness  of  this  fact.  The  bad  logic  which 
abounds  in  philosophical  discussions  consists  in  great  part  of 
conclusions  based  upon  hasty  disjunctions.  And  perhaps  no 
writer  can  hope  entirely  to  escape  from  this  error,  for  the 
process,  in  which  we  are  most  likely  to  slip,  is  at  times  un- 
avoidable. 

§  30.  (H)  We  have  nothing  now  left  but  our  old  friends 
the  so-called  Immediate  Inferences.  And  these  have  given 
cause  for  scruple  ;  doubt  extends  not  only  to  the  nature  and 
principle  of  their  procedure,  but  even  attaches  itself  to  their 
actual  existence.  If  they  are  mere  tautologies,  rearrange- 
ments of  words  without  alteration  of  ideas,  they  can  not  be 
inferences.  And  some  of  them  appear  to  be  little  else.  To 
argue  from  "  A  is  B  "  to  "  Some  B  is  A  "  gives  rise  to  suspicion, 
and  that  suspicion  is  deepened  if  we  infer  that  B  Is  equal  to  A 
because  A  is  equal  to  B,  or  that  A  must  be  to  the  left  of  B, 
since  B  is  certainly  to  the  right  of  A.  We  may  ask  in  these 
cases  what  new  conclusion  comes  from  the  process.  On  the 
other  hand  if,  given  that  A  is  B,  we  are  offered  the  assertion 
"  Not-A  is  not  B,"we  decline  to  receive  this  erroneous  addition. 
We  should  call  it  a  bad  inference,  and  should  hence  be  com- 
promised when  invited  to  deny  that  the  legitimate  "  Not-B  is 
not  A  "  is  an  inference  at  all. 

We  need  not  enter  on  the  thankless  task  of  enquiring  in 
each  case  if  the  inference  is  real  or  is  simply  circular.  For  no 
logical  principle  is  involved  in  this  controversy,  and  it  will  be 
enough  to  show  that,  given  the  validity  of  the  immediate 
inferences,  we  have  already  laid  down  those  types  of  argument 
under  which  they  will  fall.  In  any  case  they  will  make  no 
addition  to  those  classes  of  reasoning  which  we  have  already 
reviewed. 

§  31.  Where  the  so-called  inference  repeats  the  assertion 

2  C  2 


388  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

from  which  it  started,  there  is  nothing  to  be  said.  From  A  =  B 
to  proceed  by  proof  to  B  =  A  is  an  impossible  process.  In 
each  case  you  possess  the  same  relation  of  A  to  B,  and  the 
order  in  which  you  take  those  terms  is  perfectly  irrelevant. 
Hence  the  alteration  which  is  made  is  psychological,  not 
logical,  and  is  concerned  with  nothing  but  the  verbal  ex- 
pression. 

Let  us  take  another  case  where  the  process  seems  doubtful. 
It  is  not  easy  to  answer  off-hand  the  question,  if  "  No  B  is  A"  is 
a  mere  repetition  of  "  No  A  is  B,"  or  if  "  Some  B  is  A  "  is  a  real 
advance  on  "  A  is  B."  But  suppose  that  these  are  inferences, 
they  both  fall  under  heads  which  we  know  already.  If,  given 
one  truth,  you  perceive  another  implied  or  contained  in  it,  this 
process  is  analysis  followed  by  abstraction.  And  what  falls 
outside  this  is  an  inference  from  disjunction.  If  to  perceive 
for  instance  that  Not-B  is  not- A,  an* experiment  is  required 
which  goes  beyond  the  inspection  of  "  A  is  B,"  the  process  in 
that  case  will  be  indirect  and  the  reasoning  apagogic.  I  will 
illustrate  these  general  observations  by  some  remarks  on  the 
detail  of  Immediate  Inferences. 

§  32.  If  we  consider  first  the  immediate  conclusions  from 
affirmative  judgments,  we  shall  find  a  good  deal  which  excites 
our  wonder.  The  ambiguity  which  besets  the  word  "  some  " 
brings  disgrace  on  this  part  of  the  traditional  logic  ;  and 
behind  this  ambiguity  there  is  something  hidden  which  will 
hardly  bear  the  light.  Let  us  take  the  judgment  as  assertorical, 
"All  A  is  B."  What  is  it,  we  may  ask,  that  the  inference 
gives  us,  save  this  same  relation  over  again }  Take  the 
judgment  first  in  extension  as  "  All  the  A's  are  all  the  B's  ;  "  is 
it  any  news  to  be  told  that  also  "  All  the  B's  are  all  the  A's  "  ? 
Is  it  not  the  old  relation  once  more  }  Or  if  you  know  that  the 
A's  are  a  part  of  the  B's,  are  you  further  advised  when  you 
learn  that  a  part  of  the  B's  are  the  A's  }  If  again  from  "  All 
the  B's  are  all  the  A's  "  I  am  ordered  to  conclude,  that  they  are 
at  least  a  part  of  the  B'j-,  I  must  ask  for  information.  To  what 
am  I  committed  by  this  doubtful  formula  }  If  it  means  that  a 
collection,  being  taken  distributively,  is  taken  distributively, 
that,  if  I  have  seen  a,  and  have  also  seen  b,  and  also  seen  Cy 
I  must  therefore  have  seen  each — then  where  is  the  inference  ? 


Chap.  II.]  FRESH   SPECIMENS   OF   INFERENCE.  389 

But  if  it  means  that  what  is  true  of  a  lot  is  true  of  some  or 
each  component  part  of  that  lot — then  the  inference  is  vicious, 
and  the  lot  again  is  perhaps  hardly  taken  in  its  extension. 
And  if  I  am  invited  finally  to  argue  that,  since  I  am  certain 
of  each,  I  therefore  am  certain  at  least  of  some,  since  that  may 
be  true  even  though  I  can  not  be  sure  of  each,  then  I  must 
answer  that  you  seem  to  be  suggesting  that  I  should  doubt 
my  premise  upon  the  ground  of  its  certainty. 

If  again  you  do  not  take  the  predicate  in  extension — if  you 
argue  Because  all  the  A's  have  a  quality  B,  therefore  some 
things  which  have  the  quality  are  all  the  A's — I  can  not  see  how 
you  have  advanced  one  step.  You  know  already  that  there 
are  things  which  have  a  quality  B  with  a  quality  A,  and  what 
more  do  you  learn  ?  Your  "  at  least  some  B's  are  A's  "  is  not  a 
positive  conclusion  at  alL  If  it  is  neither  tautologous  nor 
downright  false,  it  is  a  caution  to  yourself  7iot  to  make  an 
inference  of  a  certain  kind.  It  says,  "  I  have  a  certain  relation 
which  I  must  not  go  beyond  ;  to  dispense  with  the  *  some ' 
would  be  wanton  temerity,  and  to  say  'at  most'  would  be 
unauthorized  despair.  The  right  state  of  mind  is  a  doubtful 
hope,  or  an  expectant  ignorance."  But  this  is  not  to  infer, 
or,  if  this  is  inferring,  it  is  an  inference  which  in  the  same 
breath  concludes  that  we  must  not  make  an  inference. 

And  if,  while  we  keep  its  assertorical  character,  we  try  to 
read  the  whole  judgment  according  to  intension,  we  fare  no 
better.  It  is  a  fact  that  the  attribute  B  attends  upon  the 
subject  or  attribute  A.  Can  we  proceed  from  this  to  anything 
more  than  a  vain  repetition  .'*  To  bring  in  our  "  at  least "  is  a 
futile  expedient,  for  it  merely  reminds  us  of  what  we  did  not 
say,  and  of  what  we  must  7tot  say,  viz.  that  B  is  never  to  be 
found  without  A.  But  this  is  not  making  a  good  inference  ; 
it  is  forestalling  a  bad  one. 

And  if  you  reply,  "  To  forestall  a  bad  inference  is  to  infer. 
For  how  else  should  I  know  that  my  inference  was  bad,  unless 
after  making  it  I  compared  it  with  my  datum  in  an  ideal 
experiment  ?  My  "  at  least  some  B  is  A "  does  mean  that 
besides  there  is  a  mere  possibility.  And  the  knowledge  of  this 
possibility,  which  to  me  is  not  more  and  must  not  be  thought 
more,  how  else  should  I  get  it  but  by  an  inference  ?  " — then 


390  THE   PRINCIPLES  OF   LOGIC.  [Bk.  III.  Pt.  I 

I  answer  that  I  am  ready  to  accept  your  contention,  for  you 
now  have  yourself  admitted  that  your  conclusion  is  not 
assertorical,  but  is  problematic. 

§  33.  The  truth  is  that,  if  you  keep  to  categorical  affirma- 
tives, your  conversion  or  opposition  is  not  rational,  but  is 
simply  grammatical.  The  one  conversion  which  is  real  inference 
is  a  modal  conversion,  and  that  presupposes  a  hypothetical, 
character  in  the  original  judgment.  I  will  not  labour  to  prove 
this  last  observation,  but  will  proceed  to  show  that  a  hypotheti- 
cal judgment  can  be  converted  modally. 

It  can  not  be  converted  in  any  other  way.  In  "  given  A 
then  B  "  you  experiment  with  A,  and  your  result  is  B.  But 
you  can  not,  by  simply  taking  B,  experiment  with  that,  and  so 
get  as  a  result  its  relation  to  A.  This  I  think  is  obvious,  and 
if  in  despair  we  fall  back  on  our  old  device  and  bring  in 
"  some  at  least,"  we  shall  get  no  further.  We  shall  succeed  in 
saying  "  Given  B  you  have  A,  if  you  suppose  the  case  where 
A  has  given  B."     This  is  barren  tautology. 

The  real  conclusion  is  "  B  may  be  A,"  but  this  once  again 
may  be  reduced  to  mere  words.  If  you  start  with  "  Arsenic 
creates  such  symptoms,"  and  conclude  "  The  symptoms 
possibly  have  come  from  arsenic  ; "  or  if  you, begin  with  "  Any 
dog  is  a  mammal,"  and  go  on  to  infer  "A  mammal  may 
be  a  dog  " — it  is  possible  that  still  you  are  drifting  between 
the  Scylla  of  false  inference  and  the  Charybdis  of  verbiage. 
It  is  assumed  that  you  mean  to  go  beyond  the  truth  you 
started  with,  and  that  you  are  not  content  with  the  impotent 
result,  that  the  symptoms  are  arsenical  upon  the  condition 
that  arsenic  has  caused  them.  You  really  mean  that  they  may 
or  may  not  be  arsenical,  but  that  yoit  have  some  reason  to  judge 
that  they  are  so.  And  this  is  the  point ;  for  you  do  not  judge 
directly  of  the  real  facts ;  you  do  not  conclude  by  a  vicious 
extension  that,  given  some  other  drug,  you  might  have  the 
same  symptoms ;  nor  again,  by  an  orthodox  but  imbecile 
process,  that,  since  arsenic  must  be  mortal,  its  administration 
at  least  may  be  the  cause  of  death.  This  is  not  your 
meaning,  and  you  would  be  sorry  to  be  understood  as 
conveying  such  frivolity.  Your  real  judgment  is  about  your 
own  grounds  of  belief  and  disbelief,  and  is  only  indirectly  an 


Chap.  II.]  FRESH   SPECIMENS  OF  INFERENCE.  39 1 

assertion  about  facts.  That  the  death  may  have  come  from 
arsenic  can  mean,  that,  among  the  possibilities  of  death  which 
are  otherwise  unknown,  we  can  specify  this  one.  And  you 
perhaps  meant  to  say  this  ;  but  it  is  more  likely  that  you 
meant  to  say  something  else.  For  you  knew  nothing  before 
about  arsenic  as  a  possible  cause  of  the  death,  except  that  you 
had  no  more  reason  to  believe  in  it  than  in  anything  else. 
But  now,  from  the  knowledge  that  it  does  produce  death  with 
certain  symptoms,  you  can  make  an  inference.  You  have 
that  reason  in  favour  of  its  chance  when  you  seek  the  most 
probable  cause  of  the  death.  Among  all  the  possibilities  this 
alone  has  extra  weight,  and  the  weight  turns  the  scale.  The 
symptoms  may  or  may  not  be  arsenical ;  but  in  favour  of  the 
former  we  have  at  least  the  consideration  that  arsenic  certainly 
would  produce  them.  There  is  so  much  more  probability  in 
favour  of  arsenic  than  there  is  in  favour  of  any  other  cause. 
And  this,  I  think,  was  what  you  really  intended  to  convey. 

And  if  the  conversion  has  this  modal  character,  it  then 
will  imply  an  inference  based  upon  the  disjunction  of  possible 
alternatives. 

§  34.  This  argument  from  certainty  to  probability  is,  I  think, 
the  real  sense  which  underlies  the  conversion  of  affirmative 
judgments.  We  may  be  told,  in  answer  to  our  charge  of  frivo- 
lity, that  such  conversion  and  opposition  are  a  valuable  agent 
in  education,  and  that  therefore  the  orthodox  logic  in  this 
point  can  not  be  wholly  absurd.  Most  absurd,  I  reply,  in  the 
doctrine  that  it  inculcates,  but  possibly  useful  because  mis- 
understood into  something  rational.  It  can  not,  I  should  say, 
much  profit  a  pupil  to  be  taught  that,  if  "every  dog  is  a 
mammal,"  he  may  argue  that  "  some  mammals  are  therefore 
dogs,"  and  from  this  make  his  way  to  the  triumphant  con- 
clusion "  Some  dogs  are  mammals"  (cf  Lotze,  Logik^  §  81).  I 
should  have  thought  that  it  might  have  been  better  to  tell 
him  that,  unless  he  has  special  information  before  him,  he  can 
not  reason  straight  from  the  attribute  to  the  subject  or  from 
the  consequence  to  the  ground  He  might  be  told,  I  should 
have  fancied,  that  the  presence  of  the  former  was  a  sign  to  his 
mind,  which  so  far  certainly  increased  the  probability  of  the 
latter,  but  still  could  not  prove  its  actual  presence.     This  is 


392  THE  PRINCIPLES  OF  LOGIC.  [Bk.  III.  Pt.  L 

what  he  must  learn,  if  he  really  learns  anything  else  than 
folly,  and  this  he  has  to  learn  in  spite  of  his  teaching.  It  is 
here  as  elsewhere  with  the  uneducated  professional.  He  is 
pledged  to  the  creed  that  truth  can  not  be  imparted  until  lost 
in  a  medium  of  superstition  and  nonsense. 

§  35.  If  we  pass  to  the  conversion  of  negative  judgments 
and  to  conversion  by  way  of  contraposition,  we  must  modify 
these  charges.  It  can  hardly  be  'maintained  that  in  this  new 
sphere  we  have  no  frivolity ;  but  on  the  other  hand  it  can  not 
be  said  that  we  have  nothing  else.  From  "  A  is  not  B  "  there 
seems  really  a  passage  to  "  B  is  not  A."  This  no  doubt  may 
be  questioned ;  we  may  be  told  that  we  knew  before  that  A 
and  B  were  incompatible,  and  that  now  we  but  know  that  B 
is  incompatible  with  A ;  we  thus  have  the  same  relation  with 
a  grammatical  difference.  But  this  view  I  take  to  be  in- 
correct. It  is  true  no  doubt  that  in  negation  we  may  be  said 
to  experiment  with  both  our  terms,  while  in  affirmative  judg- 
ment we  have  but  the  first.  Still  the  result,  arrived  at  by  the 
negative  experiment,  is  not  the  incompatibility  of  A  and  B. 
We  find  that,  given  A,  B  can  not  be  there ;  but  as  to  what 
will  happen  when  B  is  supposed,  we  have  no  information. 
Hence  the  relation  arrived  at  is  so  far  onesided. 

How  then  do  we  gain  the  other  side  of  this  truth  ?  Most 
certainly  not  by  any  general  principle,  for  that  principle  itself 
must  first  be  got  by  the  process  in  question.  The  process 
must  consist  in  another  experiment,  which  takes  B  as  real 
and,  suggesting  A,  again  finds  exclusion.  The  essence  of  the 
inference  is  open  to  doubt.  It  might  be  treated  as  the 
explicit  perception  of  a  new  relation,  got  by  abstraction  from 
an  implicit  whole  ;  but  I  should  prefer  to  take  it  as  apagogic. 
Suppose  B,  then  A  is  excluded  or  is  possible.  First  let  it  be 
possible,  and  then  A  may  be  B  ;  or  again  B  may  be  not-B,  for 
B  can  be  A  and  A  is  not  B.  Thus  we  prove  indirectly  that  B 
excludes  A  and  that  the  two  are  incompatible.  It  is  by 
virtue  of  the  same  apagogic  process,  that  we  are  able  to 
reason  from  the  absence  of  the  consequent  to  the  absence  of 
the  ground. 

§  36.  This  brings  us  to  contraposition,  and  here  without 
doubt  we  have  real  inference.     Given  "A  is  B,"  we  can  be 


Chap.  II.]  FRESH   SPECIMENS  OF   INFERENCE.  393 

sure  that  not-B  is  not-A ;  yet  we  can  not  be  supposed  to  see 
this  immediately.  The  process  is  indirect,  and  rests  upon 
disjunction.  Not-B  must  either  be  A  or  not-A,  but  A  is 
impossible,  because,  given  A,  we  must  have  B  ;  and  by  con- 
sequence B  might  exclude  itself,  or,  if  absent,  must  be  there. 
This  conclusion  removes  the  alternative  "  Not-B  is  A  ; "  and, 
since  but  one  possibility  remains,  that  is  therefore  actual,  and 
hence  not-B  is  not-A.  We  might  desire  something  better 
than  such  an  indirect  reasoning,  which  depends  on  the  mere 
exhaustion  of  alternatives  ;  but  the  desire  would  not  easily 
find  its  satisfaction. 

§  37.  I  may  end  by  mentioning  the  so-called  Inference 
through  added  Determinants.  If  we  are  sure  that  a  negro  is 
a  fellow  creature,  we  may  go  on  to  argue,  A  negro  who  is 
in  suffering  is  a  suffering  fellow  creature.  Modern  prejudice 
takes  the  truth  as  a  tautology,  and  would  deny  the  very 
existence  of  the  inference ;  but  against  this  we  may  set  the 
moral  prejudice,  which,  admitting  the  existence  of  the  reason- 
ing process,  practically  refuses  the  conclusion.  The  process  is 
certainly  vicious  in  form,  for  the  addition  may,  so  to  speak 
chemically  unite  with  the  terms  it  is  applied  to,  and  may  form 
two  components  which  are  incompatible.  A  lie  is  a  bad 
action,  but  it  is  only  in  rhetoric  that  a  virtuous  lie  is  a  virtuous 
crime.  So  "  friends  are  welcome,"  but  "  friends  in  adversity  " 
may  find  their  added  determinant  makes  a  change.  The 
form  of  this  inference,  it  is  clear,  will  not  stand,  and  it  is  better 
to  reduce  it  to  two  main  types.  In  one  of  these  we  say  "  A 
under  any  condition  is  B,  C  is  A  conditioned,  and  therefore  C 
is  B."  In  the  other  we  betake  ourselves  to  the  Third  Figure, 
and  abstain  in  the  conclusion  from  elision  of  the  middle.  "  A 
is  B,  A  is  C,  therefore  CAB  is  true,"  or  "  This  negro  is  a  fellow 
creature,  and  this  negro  suffers,  hence  we  have  in  this  negro 
a  suffering  fellow  creature." 

The  same  liberty  of  leaving  the  whole  construction  gives 
the  rational  solution  of  another  puzzle.  "  Because  a  horse  is  an 
animal,  the  head  of  a  horse  is  the  head  of  an  animal  "(Jevons, 
p.  18).  If  this  argument  can  not  be  reduced  to  syllogism,  it  is 
because  the  syllogism  has  first  crippled  itself  The  attributes 
of  having  a  head  and  being  an  animal  are  united  in  a  horse, 


394  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I 

and  you  conclude,  in  the  third  figure,  that  Under  some  con- 
ditions an  animal  has  a  head  ;  or,  without  elimination,  that.  In 
the  case  of  a  horse  an  animal  has  a  head.  But  this  differs 
from  the  result  given  by  Professor  Jevons  in  nothing  except 
grammatical  form.  The  whole  difficulty  has  arisen  from  the 
supposed  necessity  of  eliding  the  middle. 

I  do  not  know  what  to  say  of  that  inference  by  way  of 
omitting  a  determinant  which  Mr.  Venn  notices  {Symbolic 
Logic,  pp.  285-6),  for  I  do  not  think  that  I  understand  it. 
"  *  Men  are  rational  mortals  ;  therefore  they  are  mortals  :' — 
Here  we  have  omitted  the  term  *  rational '  from  our  result, 
that  is,  we  have  eliminated  it.  Or  we  might  have  omitted  the 
word  *  mortal,'  by  saying  that  *  men  are  rational.'  "  But,  if  we 
did  this,  we  should  surely  be  proceeding  in  a  way  which  we 
can  not  justify.  If  our  conclusion  is  based  on  extraneous 
information  as  to  the  irrelevance  of  one  term,  that  information 
should  have  appeared  as  a  premise.  But  if  we  mean  to  rest 
on  the  bare  statement  that  we  have,  then  we  are  certainly 
illogical.  We  may  mean  that  men  "before  identified  with 
*  rational  mortals '  are  now  identified  with  an  uncertain  part 
of  the  larger  class  *  rational,'  or  '  mortal'  "  {ibid.  287) — but,  if 
so,  I  must  repeat  a  former  criticism  (§  32)  :  We  shall  have 
argued  from  my  certain  knowledge  to  my  uncertainty  and 
ignorance.  We  shall  in  effect  say,  because  I  am  sure  of  a 
thing,  therefore,  and  for  no  other  reason,  I  do  not  know  it. 
And  this  surely  will  not  do. 

We  may  object  on  other  grounds.  The  judgment  may 
become  false  if  you  remove  any  part  of  it.  "Religious 
miracles  are  pretended  facts  that  are  necessary  illusions  ; " 
try  elimination  here.  Or  test  the  process  by  Mr.  Venn's  own 
instance.  Men  would  7iot  be  rational  if  they  were  not  mortal, 
nor  would  they  be  mortal  if  they  were  not  rational ;  for  in 
either  case  they  would  cease  to  be  men.  Our  argument  has 
illustrated  a  well-known  type  of  logical  mistake.  For  men 
simply  rational  would,  metamorphosed  by  no  logical  change, 
have  risen  like  the  angels  ;  and  simply  mortal  would  have  lost 
that  foreknowledge  which  divides  them  from  the  beasts.  Each 
alternative  robs  them  of  their  human  existence ;  they  perish 
alike  before  the  nudity  of  Reason,  and  la  mort  sans  phrase. 


Chap.  II.]  FRESH   SPECIMENS  OF   INFERENCE.  395 

§  38.  The  list  of  the  so-called  Immediate  Inferences  has  not 
given  an  additional  type  of  reasoning.  They  all  fall  under 
the  previous  classes,  and  none  of  them  can  strictly  be  called 
"  immediate,"  for  none  gives  a  conclusion  without  an  operation. 
But,  if  we  leave  them  and  ask  for  the  general  result  of  the 
present  Chapter,  we  may  state  it  thus.  Apart  from  these  last, 
we  have  found  a  number  of  palpable  inferences  which  can  not 
be  brought  under  the  formula  we  laid  down  in  the  previous 
Book;  The  list  of  such  processes  may  not  have  been  exhaustive, 
but  enough  has  been  adduced  to  show  beyond  question  that 
the  general  nature  of  the  reasoning  process  has  yet  to  be 
ascertained. 


]g6  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 


CHAPTER  III. 

GENERAL  CHARACTERISTICS  OF  INFERENCE. 

§  I.  The  position  we  now  stand  in  is  briefly  this.  It  is  not 
every  inference  that  gets  a  new  relation  of  the  original  elements, 
by  means  of  a  construction  that  interrelates  them.  This  is 
not  the  universal  type  of  reasoning,  and  it  obviously  does  not 
present  us  with  its  essence.  The  ideal  operation  is  not  always 
a  synthesis  based  on  the  identity  of  given  terminal  points. 
The  place  of  such  a  construction  may  be  taken  by  processes, 
the  nature  of  which  we  have  partly  seen,  but  whose  general 
type  we  have  not  yet  asked  for.  But  we  must  delay  that  enquiry 
till  we  reach  another  chapter.  At  present  we  shall  not  take 
this  diverse  array  of  ideal  operations,  and  try  to  reduce  them 
to  common  types  ;  for,  before  attempting  this  scrutiny,  we 
may  pause  with  advantage  and  raise  some  questions. 

§  2.  And  the  first  of  these  is.  Can  we  not  at  once  say  some- 
thing general  about  the  nature  of  reasoning  }  Without  regard 
to  the  differences  which  we  have  brought  to  light,  is  there 
not  some  account  which  holds  true  of  all  of  them  ?  And  we 
answer  that  we  can  see  clearly  such  a  common  character. 
No  matter  what  the  operation  may  be,  there  is  always  some 
operation.  This  operation  is  an  ideal  experiment  upon 
something  which  is  given,  and  the  result  of  this  process  is 
invariably  ascribed  to  the  original  datum.  We  have  here  an 
application  of  the  Principle  of  Identity,  for  what  is  true  of  a 
datum  within  the  operation  of  our  ideal  experiment,  is  also  in 
some  sense  true  of  that  dattim  without  regard  to  the  experi- 
ment. This  formula  holds  good  throughout  all  our  instances, 
and  it  will  repay  us  to  consider  them  awhile  from  this  side 
and  aspect  of  their  nature. 

§  3.  In  reasoning  we  have  a  starting-place  that  is  given,  a 
subsequent  operation,  and  a  consequent  modification  of  that 


Chap.  III.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      397 

starting-place.  In  an  abstract  form  we  may  represent  it  as 
follows.  First  A,  then  A  in  ideal  experiment  becoming  Ab^ 
and  last  the  assertion  that  Ab  is  true,  unconditionally  or 
conditionally.  We  have  thus  (i)  Premises  or  premise,  (ii) 
Operation,  and  (iii)  Result.  The  first  is  A\  the  second  is 
A'^by  the  last  is  A^b.  For  what  holds  of  A  once  will  hold  of  it 
always,  and  the  quality,  which  A  gets  in  the  context  of  that 
process  which  we  represent  by  A^,  belongs  in  some  sense  to 
A  apart  from  the  process.  Our  present  task  will  be  to  verify 
this  type  throughout  all  our  examples. 

§  4.  We  may  preface  the  enquiry  by  a  reference  to  causa- 
tion. Without  discussing  the  exact  relation  which  exists 
between  the  causal  and  the  reasoning  processes,  we  may  refer 
to  something  which  they  have  in  common.  In  causation  you 
first  of  all  start  with  the  elements  called  the  "  conditions,"  the 
next  step  consists  in  the  process  of  change  which  issues  in  a 
certain  result,  and  the  whole  is  complete  when  that  which  has 
resulted  is  ascribed  to  the  original  conditions.  It  is  the  same 
with  inference.  The  result'  of  change  that  issues  from  the 
process  into  which  the  original  datum  enters,  is  ascribed  to 
that  datum.  Both  causation  and  reasoning  depend  upon 
identity,  sameness  in  spite  of  a  growth  of  difference ;  sameness 
again  which  preserves  itself,  not  by  refusing  but  by  appropria- 
ting that  difference.  Both  are  alterations  of  a  datum  which  is 
changed,  but  survives  in  its  changes  and  makes  them  its 
attributes.  In  a  future  chapter  we  shall  further  discuss  the 
relation  which  subsists  between  the  effect  of  a  cause  and  the 
conclusion  of  an  argument. 

§  5.  Returning  to  the  task  we  have  now  in  hand,  let  us 
proceed  to  the  application  of  our  general  remark.  And  let 
us  try  first  those  inferences  which  interrelate  three  terms,  and 
which  so  bring  out  a  new  relation.  In  these  we  have  first  the 
elements  of  our  construction  existing  apart,  then  we  have  the 
construction,  and  last  of  all  the  new  relation.  Take  for 
instance  "  A  to  the  right  of  B,  and  B  of  C,  and  therefore  A  to 
the  right  of  C."  We  here  have  got  (i)  two  spatial  relations, 
or  rather  two  sets  of  terms  in  relations  of  space,  and  we  may 
call  this  starting-place  reality  qualified  as  these  pairs  of 
relations.     Let  us  pass  to  the  second  step  (ii) ;  this  gives  us 


39^  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  L 

the  synthesis  of  those  very  same  terms  which  we  had  at  the 
beginning.  The  construction  certainly  is  a  difference,  but  it 
does  not  make  such  a  difference  to  our  terms  that  they  lose 
their  identity.  We  next  (iii)  perceive  a  new  relation,  the 
result  of  the  construction.  But  since  the  terms  are  the  same 
notwithstanding  the  construction,  they  are  the  same  in  respect 
of  this  further  result,  C— A.  Hence  the  real,  qualified  as 
C  —  B  B  —  A,  is  the  real  qualified  as  C  —  B  —  A,  and  that  again 
is  the  selfsame  subject  as  the  real  which  has  the  relation 
C— A.  We  have  sameness  both  within  and  without  the 
construction,  and  we  have  appropriation  of  that  construction's 
result. 

Take  another  argument,  "A  is  equal  to  B,  and  B  to  C, 
and  therefore  C  =  A."  The  whole  synthesis  of  these  terms, 
effected  through  B,  is  the  second  stage,  on  which  follows 
thirdly  the  separate  perception  A  — C.  The  result  of  the 
construction  is  taken  as  its  attribute,  and  is  so  predicated ; 
and  the  construction  itself  is  in  just  the  same  way  made  an 
attribute  of  the  terms.  A,  B,  and  C  are  the  same  in  the  con- 
struction and  with  the  result  that  it  developes,  as  they  were 
apart  from  it.  The  issue  of  the  operation  is  simply  their  own 
being. 

And  we  can  verify  this  type  in  the  common  syllogism. 
In  "  Mammals  are  warm-blooded,  men  are  mammals,  and  so 
men  are  warm-blooded,"  we  find  the  same  elements.  First 
the  separate  judgments  are  given  us  as  true ;  we  have  reality 
appearing  in  the  attribute  of  these  two  syntheses,  "man- 
mammal"  and  "mammal-warm-blooded."  Then  the  con- 
struction follows,  and  from  that  the  intuition  of  "  man-warm- 
blooded." But  the  relation  which  we  predicate  of  these 
extremes,  is  not  a  foreign  compulsion  of  their  nature.  For 
the  issue  of  the  process,  the  result  of  the  change,  has  not 
removed  their  sameness.  They  have  remained  through 
alteration,  and  accept  the  difference  as  their  proper  attribute 
and  native  possession. 

§  6.  Where  we  go  from  the  construction  not  to  a  new 
internal  relation  but  to  a  quality  of  the  whole,  our  account 
still  holds  good.  The  elements,  which  during  our  circular 
voyage  we   received  discontinuously   each   in   isolation,  first 


Chap.  III.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      399 

combined  themselves  into  a  spatial  whole,  and  then  took  on 
the  qualities  we  understand  by  "  island."  But  the  reality 
throughout  has  maintained  its  identity.  It  moved  before  our 
eyes  a  changing  show,  that  came  fresh  from  the  unknown  and 
slid  back  perpetually  into  nothingness.  To  our  judgment  it 
appeared  as  a  discrete  series  of  spatial  arrangements  ;  and  it 
was  with  this  series  that  our  reasoning  began.  That,  boldly 
relying  on  the  Identity  of  Indiscernibles,  built  up  for  us  an 
intellectual  whole,  and  that  whole  presented  us  with  certain 
qualities.  We  then  attributed  these  qualities  to  that  very 
reality  which  was  manifest  in  our  fragments  of  successive 
coast  line.  The  reality  has  certainly  both  undergone  experi- 
ments and  suffered  changes  at  our  hands.  It  is  not  what  it 
was,  and  it  yet  remains  the  same  ;  for  it  is  itself  and  more. 
It  is  the  original  subject  with  additional  attributes,  conferred 
upon  it  by  our  ideal  operations. 

We  find  the  same  when  we  pass  to  spatial  arrangement. 
Bricks  and  mortar  with  the  builder  are  here  our  premises,  the 
compound  action  and  reaction  of  the  two  may  be  called  the 
construction,  and  the  conclusion  is  the  appearance  of  the  house. 
It  may  be  doubted  how  the  elements,  which  we  had  at  the 
start,  can  survive  in  the  result ;  yet  we  can  not  but  think  that 
somehow  they  have  survived.  For  other^vise  it  would  surely 
be  false  to  say  that  the  house  is  the  effect  which  has  come 
from  these  causes.  I  admit  the  difficulty  which  attaches  to 
identity,  but  it  is  still  harder  to  believe  in  a  discontinuous 
existence  and  in  a  divided  reality.  For  if  in  the  house  you 
have  not  got  the  work  done  by  the  builder  on  a  certain 
material,  you  have  no  right  to  speak  as  if  you  had.  And 
you  could  not  even  say  that  the  house  has  appeared,  without 
synthetic  judgments  which  assume  an  identity.  If  the  reality 
has  changed,  the  same  reality  must  be  there  still,  and  if  the 
reality  has  7iot  changed,  there  has  been  no  change  whatever  ; 
for  a  sequence  of  mere  differences  would  have  nothing  it  could 
alter,  and  could  not  generate  even  the  show  of  alteration. 

And  in  the  same  way  when,  not  externally  but  simply  in 
my  head,  I  rearrange  elements  by  an  arbitrary  choice,  the 
result,  which  I  get  at  the  end  of  my  process,  is  true  of  the 
basis  from  which  I  began.     That  foundation  has  survived  and 


400  THE   PRINCIPLES   OF   LOGIC.  [Bk.  HI.  Pt.  I. 

has  got  a  new  quality  without  the  loss  of  its  own  selfsame- 
ness.  The  result  is  hypothetical,  since  my  free  action  was  no 
more  than  possible.  One  element  of  the  cause,  apart  from 
the  others,  is  but  the  hypothetical  producer  of  the  conse- 
quence, and  is  no  more  than  what  we  call  a  "  condition." 

§  7.  We  may  deal  rapidly  with  the  operations  of  addition 
and  subtraction.  We  have  the  units  arranged  in  a  certain 
manner,  and  these  are  our  material  with  which  we  begin. 
Then  follows  a  rearrangement  of  these  units,  and  a  consequent 
perception  of  another  attribute  which  also  belongs  to  them. 
Throughout  the  operation  the  units  are  identical,  and  they 
appropriate  the  result  of  the  experiment.  And  since  it  is 
assumed  that  to  them  the  experiment  can  make  no  difference, 
therefore  that  difference  becomes  a  categorical  predicate. 
The  units  with  a  quality  of  certain  integers  go  into  a  process, 
and  come  out  in  possession  of  another  quality.  Thus  by 
virtue  of  this  change  the  identical  subject  is  credited  with 
both  contexts,  or,  in  other  words,  the  two  different  arrange- 
ments, which  we  began  and  ended  with,  are  taken  as  identical. 

And  it  is  clear  that  the  same  view  holds  good  of  geometry. 
The  data  are  divided  or  are  rearranged  or  are  compounded 
with  arbitrary  fresh  surroundings,  and  from  this  manipulation 
comes  out  a  result.  But  since  the  experiment  adds  nothing 
to  the  data  nor  takes  anything  away,  since  again  the  data 
remain  the  same  throughout  the  experiment,  the  result 
becomes  their  categorical  attribute. 

§  8.  In  Comparison  it  is  easy  to  recognize  the  same  type. 
A  and  B  are  first  given  us  apart  from  their  relation.  The 
next  stage  is  the  process,  in  which  we  bring  them  together, 
and  so  perceive  a  relation  of  likeness.  The  relation  is  then 
predicated  of  A  and  B  apart  from  our  comparing  activity. 
They  are  alike  because  their  change  to  this  relation  was  no 
alien  imposition,  and  because  their  identity  has  remained 
unimpaired  throughout  the  alteration.  The  same  remarks 
apply  to  the  inference  of  Distinction. 

And  they  apply  once  more,  with  slight  modification,  to 
Dialectic  reasoning,  to  Recognition,  and  to  the  Hypothetic 
judgment.  In  all  these  we  have  but  one  premise  explicit ; 
we  start  with  AB,  and,  subjecting  this  to  an  ideal  experiment. 


Chap.  III.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      4OI 

we  are  given  ABC.  The  original  datum  is  met  by  a  function 
which  produces  a  result.  But  it  is  assumed  once  more  that 
the  synthesis  does  not  arbitrarily  add  from  the  outside  ;  and 
hence,  since  the  dattim  is  the  same  in  the  experiment  as  it 
was  beforehand,  the  result  is  taken  as  its  quality  and  attribute. 

Nor  in  passing  to  Abstraction  do  we  find  any  change. 
We  start  here  with  reality  in  the  character  of  abcd^.  This 
same  content  is  subjected  to  an  ideal  operation  as  abcd^, 
and  then  presents  us  with  a  —  d.  Upon  this  we  conclude  that 
abcd"^  is  also  ad,  or,  more  directly,  that  the  reality  is  ad. 
But  our  conclusion  would  be  false,  did  it  not  presuppose  the 
identity  of  the  subject  in  two  different  contexts. 

§  9.  In  Disjunction  lastly  we  find  once  again  this  identity. 
Whether  we  begin  with  the  alternatives  stated  as  exclusive, 
or  with  a  simple  field  of  possibilities,  makes  no  real  difference. 
We  start  with  a  subject  determined  inside  a  certain  area  of 
possible  predicates.  This  subject  then  undergoes  an  opera- 
tion which  reduces  that  area,  and  it  ends  by  seizing  on  the 
undestroyed  remainder  as  its  actual  attribute.  But  it  could 
not  do  this,  if  it  stood  outside  the  process  or  were  dissipated 
within  it  Itself  goes  there  and  is  active,  preserving  its  self, 
and  emerging  with  a  difference  which  it  refuses  to  give  up. 

The  same  character  is  seen  in  Apagogic  reasoning,  and 
again  in  that  qualification  through  rejected  suggestion,  which 
(by  employing  the  supposal  of  an  opposite)  turns  "  it  is  "  into 
"  it  must  be."  The  identity  within  and  without  the  experi- 
ment needs  here  no  indication.  And  finally  the  Immediate 
Inferences,  which  we  were  last  concerned  with,  are  not 
independent.  They  arrange  themselves  under  the  heads  we 
have  discussed,  and  our  foregoing  remarks  have  already 
dealt  with  them. 

§  10.  Our  result  so  far  is  that  inference  is  the  getting  a 
new  result  from  a  certain  datum.  The  result  is  procured  by 
an  ideal  operation  upon  this  datum,  and  when  procured 
becomes  its  predicate.  Reasoning  thus  depends  on  the 
identity  of  a  content  inside  a  mental  experiment  with  that 
content  outside.  And  so  we  find  once  again  in  the  total 
process  that  need  for  individuation,  which  we  before  discerned 
in  the  middle  construction.      Just  as  that  construction  was 

2  D 


402  THE   PRINCIPLES   OF   LOGIC.  [Be.  IIL  Pt.  I. 

insufficient  to  give  us  a  new  relation  of  the  extremes,  unless  it 
joined  them  in  an  individual  whole — so  here  the  full  process 
would  not  get  to  a  conclusion,  unless  it  possessed  an  individu- 
ality. And  it  is  made  individual  by  the  identity  of  that 
content  which  runs  right  through  it,  and  which  joins  the  final 
result  to  the  initial  starting-point.  So  much  at  least  we  are 
now  able  to  say  in  reply  to  the  question,  What  is  an  inference  ? 
And  this  beginning  of  an  answer  we  may  go  on  to  make  clearer 
by  laying  down  some  important  distinctions. 

§  II.  It  is  not  any  and  every  mental  activity  which  can 
properly  be  called  reasoning.  This  claim  could  not,  I  think, 
be  seriously  maintained,  but  it  may  perhaps  be  worth  while  to 
examine  its  nature.  We  may  be  asked  if  our  account,  so  far 
as  it  has  gone,  has  not  tacitly  admitted  such  a  sweeping 
pretension.  "  Does  not  every  ideal  activity,"  an  objector  may 
urge,  "  first  begin  with  a  datum  and,  performing  on  that  an 
ideal  operation,  so  produce  a  result  ?  Take  for  instance  judg- 
ment. Here  we  have  the  reality,  and  we  qualify  that  subject 
by  referring  to  it  a  suggested  content.  That  is  an  ideal  action, 
and  it  is  an  action  again  which  brings  about  a  change  which 
it  does  not  create  or  manufacture.  The  result  is  ascribed  to 
the  original  datum^  and  ascribed  by  virtue  of  an  ideal  opera- 
tion."    We  must  briefly  reply  to  this  mistaken  claim. 

§  12.  There  are  two  questions  we  must  endeavour  not  to 
confuse.  Each  of  them  asks  if  judgment  is  inference,  but 
each  makes  that  enquiry  in  a  different  sense.  The  first  asks 
if  all  judgments  imply  an  inference.  That  is,  does  judgment 
presuppose  and  is  it  the  conclusion  of  a  reasoning  such  as 
is  described  above  ?  That  is  the  first  question,  and  the 
second  is  quite  different.  For  the  second  enquires  if  every 
judgment  by  itself  is  an  inference,  independent  of  and  apart 
from  any  of  those  processes  which  we  have  hitherto  called 
argument.     We  will  begin  by  dealing  with  this  latter  claim. 

Suppose  for  instance  that  we  had  an  operation,  which, 
taking  X,  simply  added  on  j/  as  a  mere  suggestion  that  came 
from  the  outside,  and  then  judged  X— ;j/.  Could  we  call  that 
an  inference  ?  No  doubt  it  may  be  said  to  preserve  an 
identity :  no  doubt  again  that  it  ends  with  a  judgment,  which 


Chap.  III.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      403 

may  fairly  be  said  to  predicate  something  new  of  the  original 
datum.  No  doubt  once  more  it  is  an  ideal  activity.  But, 
notwithstanding  all  this,  it  is  not  an  inference.  Thej^-,  which 
in  conclusion  it  attributes  to  X,  is  not  in  any  sense  got  from 
X  by  an  operation  thereon.  It  is  stuck  on  from  the  outside  ; 
and  because  the  result,  ascribed  in  the  conclusion,  is  not  pro- 
cured from  the  starting-point,  therefore  this  result  is  not  a 
real  conclusion. 

§  13.  In  the  arbitrary  synthesis  of  a  suggestion  with 
reality  the  predicate  does  not  really  come  from  the  datum. 
It  thus  lacks  an  essential  character  of  inference,  the  getting  of 
the  product  on  and  from  the  premises.  We  may  try  however 
to  renew  the  attempt  in  an  amended  form.  Judgment,  we 
may  say,  is  an  inference  of  this  kind  ;  we  have  (i)  Reality 
together  with  a  suggestion,  and  beside  these  two  we  have  an 
arbitrary  power  of  junction.  These  three  elements  are  our 
premises,  and  we  have  (ii)  the  actual  union  of  these  elements, 
which  gives  (iii)  the  synthesis  of  the  predicate  with  reality — 
and  this  result  is  a  conclusion.  But  this  amended  attempt  is  as 
futile  as  the  former.  For  the  judgment  in  the  first  place  will  not 
be  categorical.  In  this  it  will  be  like  free  spatial  arrangement  ; 
so  that  the  inference,  if  there  is  one,  does  not  end  in  the 
simple  assertion  X  —y.  It  can  not  go  beyond,  "  If  X  is  treated 
in  an  arbitrary  manner  it  will  turn  to  X  —  j."  And  perhaps 
this  is  senseless.  For  in  the  spatial  arrangement  the  com- 
bination of  the  data  produced  a  new  quality,  while  here  on 
the  other  hand  it  produces — their  combination.  We  must  end 
by  writing  the  result  of  our  process,  "  X,  if  X  be  X  — ^,  must 
certainly  be  X— /."  And  there  does  not  seem  to  be  any 
inference  here. 

§  14.  I  offer  no  apology  for  pursuing  these  somewhat 
dull  enquiries,  since  it  seems  to  me  that  every  answer  we 
elicit  throws  some  light  on  our  general  doctrine.  We  have 
seen  so  far  that  judgment  is  not  inference,  and  that  a  process 
which  was  nothing  more  than  a  judgment  would  never  be 
reasoning.  We  may  now  approach  the  second  question  we 
asked  :  Is  every  judgment  part  of  an  inference  }  Does,  that 
is  to  say,  judgment  presuppose  a  process  which  must  be 
called  reasoning  ?     May  assertion  be  always  taken  as  con- 

2  D  2 


404  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

elusion  ?  This  is  really  a  somewhat  difficult  problem,  and, 
as  we  shall  have  to  recur  to  it  afterwards  (Chap.  VI.  §  1 5),  we 
may  content  ourselves  here  with  some  brief  remarks. 

§  15.  Some  judgments,  we  know,  do  involve  a  reasoning. 
We  saw  that  this  held  of  hypothetical,  since  the  supposition 
that  A  is  real,  is  itself  an  ideal  operation  on  this  content. 
For,  in  the  union  with  reality,  A  is  met  by  a  function  of 
synthesis  and  so  developes  a  new  connection.  And  again  if 
we  take  those  common  judgments  which  go  beyond  presenta- 
tion— I  mean  those  extensions  of  sense  which  supply  us  with 
the  past  or  with  the  unseen  present — they  are  all  inferential. 
They  imply,  as  we  saw,  an  ideal  operation,  and  it  was  for  that 
reason  that  we  called  them  "  synthetic."  Nay,  when,  leaving 
these,  we  come  down  in  the  end  to  those  judgments  which 
assert  about  present  perception — the  class  we  thought  fit  to 
call  "  analytical  " — even  here  it  may  seem  we  are  dependent 
on  reasoning.  For  these  assertions  are  based  on  a  process  of 
mutilation.  They  are  all  abstractions,  and  abstraction,  we 
now  know,  is  a  kind  of  inference.  So  that,  resting  on  these 
grounds,  we  clearly  have  got  some  cause  to  maintain  that 
judgment  is  never  separable  from  reasoning. 

§  16.  But  there  is  ground  on  the  other  side  from  which  we 
might  deny  this  thesis.  "  Admitted,"  we  might  say,-  ''  that 
every  judgment  can  be  turned  into  a  kind  of  inference  by  a 
suggestion  of  the  opposite,  yet  all  judgments  do  not  undergo 
this  operation.  In  the  first  place  the  operation  may  be 
wholly  circular  (cf  Chap.  II.  §  28),  and  hence  illusory  :  and 
then,  apart  from  this  objection,  in  very  many  cases  it  does  not 
exist  at  all.  These  cases  so  far  will  be  free  from  all  reasoning. 
And  now,  passing  from  this  point,  let  us  take  in  hand  a  more 
real  difficulty.  We  admit  that  all  judgments,  though  they 
may  not  combine,  at  least  must  mutilate ;  but  it  does 
not  follow  that  they  therefore  infer.  \  Mutilation '  is 
ambiguous,  for  you  may  perform  the  operation  or  may 
simply  accept  it.  A  judgment,  that  is,  may  either  start  with 
something  given,  and  by  working  on  this  may  extract  an 
isolated  and  abstract  product,  and  this  would  clearly  be 
inference  ;  or  on  the  other  hand,  instead  of  selecting,  the 
judgment  may  receive.     If  the  original  whole  has  never  been 


Chap.  Ill]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      405 

given  to  the  judgment,  if  the  judgment  takes  up  a  foreign 
suggestion  which  itself  is  mutilated,  then,  although  in  con- 
clusion we  affirm  an  abstraction,  yet  we  have  not  abstracted, 
and  the  result  for  iis  will  not  be  a  conclusion." 

§  17.  "  For,"  we  might  continue,  "  you  should  consider  it  so. 
You  can  not  reason  categorically  unless  you  start  with  a  given, 
and  unless  this  given  premise"  contains  a  judgment.*  If  there- 
fore all  judgment  depended  on  inference,  you  never  would  get 
to  an  ordinary  judgment.  And  the  only  way  in  which  to 
escape  this  circle,  is  to  begin  with  judgments  that  imply  no 
reasoning.  Nor  is  this  impossible,  for  you  may  have  a  result 
which  involves  selection,  and  yet  you  may  never  yourself  have 
selected.  An  abstracted  content  can  be  conveyed  to  your 
mind,  though  you  have  not  worked  on  the  raw  material. 
The  testimony  received  from  others  is  an  instance  ;  and  then, 
apart  from  the  reasoning  of  other  men's  intellects,  you  have 
your  own  senses.  Judgment  rests  in  the  end  on  suggestions 
of  sense,  and  these  suggestions  are  never  uniform.  For  we 
do  not  feel  one  equable  and  steady  flow,  we  are  not  in  con- 
tact with  a  level  surface  ;  the  judgment  does  not  come  down 
unsolicited,  and  compose  at  random  its  spontaneous  junctions. 
This,  -if  it  were  possible,  would  be  to  reason  without  reason. 
But  it  is  not  possible.  Before  judgment  appears  there  are 
prominent  points  in  the  suggestions  of  the  senses.  A  stands 
above  the  level  and  with  it  stands  B.  Together  they  knock 
at  the  door  of  judgment,  which  admits  them  together  and 
keeps  back  the  rest.  The  result  may  thus  present  an  ideal 
synthesis,  an  intelligible  abstraction  ;  but  the  process  is  no 
selection  of  the  reason.  It  is  bare  natural  selection,  where 
the  fittest  have  survived  and  where  the  strongest  are  most  fit. 
And  hence  the  conclusion,  for  the  intellect,  is  the  work  of  chance. 
The  mind  has  not  embraced  the  persuasion  of  argument,  but 
has  yielded  to  the  insistance  and  the  emphasis  of  sense." 

§  18.  Such  is  the  answer  we  might  make  to  the  claim  of 
all  judgment  to  stand  as  inference ;  and  in  another  Chapter 
we  shall  have  to  weigh  the  worth  of  this  denial.  But  we  can 
not  pause  to  consider  it  here,  and  must  be  content  with  a 

*  This  statement  must  be  taken  subject  to  the  explanation  given  in 
Chap.  VI.  §  15. 


406  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

partial  answer  to  our  questions.  All  judgment. is  hot  in- 
ference, if  mere  judgment  claims  a  position  as  inference.  So 
much  is  certain.  But  when  asked  if  judgment  does  not  pre- 
suppose inference,  if  in  short  the  two  activities  are  not  diverse 
stages  of  a  single  function,  we  can  not  yet  give  an  answer. 
We  have  however  shown  some  reason  for  considering  them  as 
separate,  at  least  for  the  present. 

Judgment  then  is  not  inference,  and  reasoning  is  not  the 
same  as  intellectual  activity.  We  must  now  go  on  to  consider 
a  narrower  claim.  Has  all  Redintegration  a  right  to  assume 
the  title  of  inference  ? 

§  19.  Every  reproduction  is  clearly  a  function  which  starts 
from  a  basis  and  gets  a  new  result.  And  some  reproduction 
of  course  is  inference.  Where,  AB  being  given,  C  is  supplied 
and  then  attributed  as  a  predicate  to  AB,  we  have  a  kind  of 
reasoning  with  which  we  are  now  familiar.  An  ideal  whole 
is  produced  by  a  process,  and  a  judgment  follows  from  this 
ideal  construction.  And  if  redintegration  always  had  this 
character,  the  question  if  it  always  might  call  itself  inference, 
could  be  answered  at  once  and  answered  affirmatively. 

But  there  are  other  reproductions  which  are  far  from 
appearing  to  possess  this  character.  Redintegration  does  not 
always  seem  to  result  in  judgment.  An  object  may  excite 
vague  feelings  of  pleasure  or  a  dim  sense  of  pain,  but  these 
feelings  need  not  be  attributed  to  that  object.  Their  content 
is  not  always  taken  apart  from  their  existence,  and  applied  to 
the  thing  as  one  of  its  adjectives.  They  may  remain  my  feelings, 
mere  psychical  phenomena,  which  are  together  with  the  object 
but  form  no  part  of  it.  Hence  the  process  has  no  right  to  call 
itself  inference.  For  it  does  not  end  in  a  judgment ;  the 
starting-point  does  not  survive  in  the  process,  maintaining  its 
identity  and  appropriating  the  difference.  We  simply  pass 
from  it  to  another  existence  which  is  taken  as  existing  on  a 
level  with  the  first.  This  process  is  on  the  one  hand  ideal,  in 
the  sense  that  it  advances  on  the  strength  of  a  connection 
between  universals.  But  on  the  other  hand  it  is  not  logical, 
since  the  universal,  brought  in  by  the  ideal  connection,  is  not 
used  as  a  content  which  is  bestowed  upon  the  original  object 


Chap.  III.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      407 

and  particularized  by  that  reference.  The  universal  on  the 
contrary  is  allowed  to  become  an  independent  fact,  in  which 
the  content  is  one  with  the  existence,  and  where  the  particular 
character  is  supplied  psychologically  from  my  whole  state  of 
mind.  There  is  hence  no  logical  individuation.  What  unity 
there  is  does  not  fall  within  a  developement  of  the  datum 
through  one  process  of  change.  It  falls  simply  within  my 
feeling  self;  and  the  result  is  a  conjunction  which  is  no 
connection. 

It  is  useless  to  object  that  the  result  in  the  end  may  be  a 
judgment  which  affirms  the  existence  of  this  mere  conjunction 
in  my  soul.  For  that  result  will  be  no  inference  from  the 
original  datum.  You  may  say  that  we  certainly  have  got  our 
conjunction  from  the  datum,  but  after  all  that  dattcm  does  not 
survive  in  it.  And  so  we  have  not  got  a  content,  we  have  not 
got  a  predicate,  our  result  is  not  ideal,  nor  is  it  a  conclusion. 
And  when  starting  again  from  this  mere  psychical  fact  you  go 
on  to  a  judgment,  then,  let  that  be  an  inference,  it  has  not 
been  inferred  from  the  content  we  began  with.  It  has  come 
from  a  fact  whose  existence  has  supervened. 

§  20.  This  discussion,  I  fear,  may  prove  hard  to  follow ; 
and  the  reader  who  finds  more  than  moderate  difficulties,  had 
better  pass  on  to  the  following  chapter.  For  we  are  now 
about  to  raise  another  question,  both  important  and  relevant, 
but  not  essential  to  the  understanding  of  the  sequel. 

There  is  an  answer  we  might  give  to  the  foregoing  section. 
Admitted,  we  might  say,  that  some  redintegration  exists,  the 
final  result  of  which  is  not  logical,  yet  the  process  itself,  with 
its  immediate  product,  is  still  an  intellectual  inference.  All 
reproduction  will  in  that  case  be  reasoning. 

We  objected  in  our  Chapter  on  Association,  to  the  formula 
we  found  laid  down  by  Wolff,  on  the  ground  that  reproduction 
went  beyond  perceptmts.  And  on  this  very  ground  we  have 
just  objected  to  taking  the  process  everywhere  in  the  character 
of  inference.  The  unity  of  the  process  we  found  might  be 
other  than  the  individuality  of  cognition.  But  a  doubt  may 
now  be  raised  as  to  whether  this  result  is  after  all  not  mis- 
taken, and  it  may  be  urged  that,  at  bottom,  the  recall  and 
reconstruction  are  purely  intellectual. 


40S  THE   PRINCIPLES  OF   LOGIC.  [Bk.  III.  Pt.  I. 

Let  US  try  to  state  this  possible  contention.  It  is  admitted 
on  both  sides  that  an  object,  once  accompanied  by  certain 
feelings,  may,  when  it  is  either  reinstated  ideally  or  once  again 
presented  to  sense,  bring  in  those  feelings.  The  issue  is 
this — Are  the  feelings,  as  such,  reproduced  or  produced  }  We 
have  assumed  so  far  that  the  former  is  true,  but  our  assumption 
admits  of  being  traversed  thus.  Feelings,  it  might  be  urged, 
can  not  be  recalled  unless  made  universals  ;  and  this  un- 
conscious abstraction  suggests  the  presence  of  intellectual 
work.  For  suppose  that  when  the  object  was  presented,  it, 
together  with  the  feeling,  engaged  our  attention.  This  mere 
attention  will  be  apprehension,  it  will  imply  selection  and 
rudimentary  judgment,  and  this  alone  and  by  itself  will  set 
up  between  the  elements  a  logical  connection.  It  will 
make  the  whole  perceptive,  so  that  now,  given  one  part,  the 
rest  will  follow.  Hence  the  feelings  are  recalled  as  they  are 
for  perception,  and  that  process  is  inference.  They  certainly 
come  to  us  as  psychical  facts,  but  this  final  result  falls  outside 
the  inference^  and  is  a  mere  psychological  addition. 

§  2 1.  Let  us  further  explain.  We  must  remember  that  every 
psychical  phenomenon  is  complex ;  for  on  the  one  hand  no 
perception  is  without  some  tone  of  feeling,  and  every  feeling 
on  the  other  hand  is  partly  perceptive,  and  has  a  content,  a 
character,  a  quality  that  we  recognize.  Now  suppose  that 
this  perceptive  side  of  the  feelings  was  attended  to  together 
with  the  object,  in  that  case  the  object  will  recall  it  by  reason- 
ing, and  will  supplement  itself  by  this  inferred  content.  This 
is  inference,  but  it  still  falls  short  of  what  is  wanted,  for  it  does 
not  account  for  the  side  of  mere  feeling.  How,  it  may  be 
objected,  do  you  get  back  to  that }  If  you  do  it  by  redin- 
tegration, then,  after  all  and  in  the  end,  you  have  been  forced  to 
admit  the  reality  of  what  you  denied,  a  reproduction  that  was 
not  logical. 

And  this  is  the  issue.  The  view,  which  we  are  here  attempt- 
ing to  work  out,  would  admit  that  such  reproduction  would 
not  be  logical,  but  then  it  would  deny  that  such  reproduction 
exists.  It  would  urge  in  opposition  that  it  is  the  perceptive 
side  of  the  feeling  which  is  reinstated,  and  that  this  pro- 
duces actual  feeling   dii^ectly  and  not   through  reproduction. 


Chap.  III.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      409 

The  perceptive  side  may  be  particularized  first  by  the 
psychical  context  into  which  it  is  brought,  but  this  is  not  the 
point.  The  point  is  that  it  works  directly  on  the  soul,  and  by 
that  working-  causes  an  actual  feeling  which  is  like  the  original. 
Thus  the  old  feeling,  as  feeling,  is  in  no  sense  reinstated  ;  but 
the  real  fact  is  that  the  soul  is  such,  or  has  become  such,  that, 
without  restoration  or  redintegration,  and  by  nothing  at  all 
but  simple  reaction,  it  responds  to  the  idea  with  an  outcome 
of  feeling.  And,  if  this  account  is  true,  a  restriction  has  saved 
us.  The  feeling  is  not  the  conclusion  of  an  inference,  but 
falls  wholly  without  it  as  a  mere  psychical  effect.  And,  if  so, 
the  actual  reproduction  is  purified  from  feeling,  and  remains 
in  the  character  of  intellectual  connection. 

§  22.  I  think  that  this  view  deserves  careful  attention,  but 
I  must  not  be  understood  as  adopting  it  wholly.  It  is  not 
that  I  doubt  the  reality  of  the  psychical  process  which  it 
describes ;  for  I  am  sure  that  in  some  cases  that  process  exists, 
and  its  existence  has  somewhat  important  bearings.  The 
confusion  for  instance  which  in  English  Moral  Philosophy 
besets  the  word  "  motive,"  arises  mainly  from  a  false  assump- 
tion on  this  very  point.  And  that  confusion  disappears  when 
we  distinguish  between  the  idea  itself  and  its  psychical  effect 
(cf  Ethical  Studies,  Essay  VII.). 

But  it  is  one  thing  to  hold  that  a  process  exists,  and  it  is 
another  thing  to  deny  the  existence  of  any  other  possible 
process ;  and  here  I  hesitate.  We  might  explain  perhaps 
every  phenomenon  offered,  on  the  view  that  reproduction  is 
always  logical.  This  view  in  the  hands  of  those  who  espouse 
the  cause  of  the  intellect  and  are  champions  of  its  primacy, 
would  be  a  weapon  perhaps  not  easy  to  withstand,  and  which 
would  make  short  work  of  many  difficulties.  But  then  in  some 
cases  the  explanation  might  force  the  facts.  And  again  any 
inference  from  the  universal  character  of  what  is  reproduced 
to  the  logical  nature  of  the  reproductive  process,  would 
appear  to  me  to  be  questionable.  The  logical  is  universal, 
but  I  am  far  from  sure  that  the  universal  must  be  logical. 

And  I  doubt  on  another  point.  This  simplification  might 
be  premature ;  for  suppose  we  got  down  to  an  ultimate  true 
doctrine  of  the  relation  between  the  elements  of  our  nature, 


410  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

and  suppose  we  saw  clearly  how  the  intellect  stands  to  the 
emotions  and  the  will  (if  there  really  is  a  will) — are  we 
sure  that  this  weapon  would  any  longer  be  wanted,  and 
that  the  difficulties  would  keep  the  form  that  they  now  wear  ? 
To  this  doubt  I  can  only  allude  in  passing. 

But  however  we  settle  the  questions  just  raised,  we  are 
certain  of  one  thing  in  respect  to  inference.  The  mere  result 
of  feeling,  not  attributed  to  an  object,  is  never  a  conclusion. 
Whether  produced  by  reinstatement,  or  not  so  produced, 
in  neither  case  will  it  come  straight  from  reasoning.  For  in 
the  latter  case  it  will  fall  outside  the  process,  while  in  the 
former  case  the  process  is  no  inference.  And  with  this  we 
may  proceed  to  another  enquiry. 

§  23.  A  result  of  mere  feeling  we  saw  could  not  be  an 
inference,  since  it  was  not  ideal.  But  the  result  of  imagination^ 
it  may  now  be  urged,  is  often  ideal.  It  may  keep  itself 
distinct  from  mere  emotion  and  desire,  and  may  present  us* 
with  a  pure  perceptional  series.  In  such  a  case  as  this  can 
imagination  be  called  inference  } 

We  must  deal  briefly  with  this  question,  for  it  tends  to 
divert  us  to  matters  of  great  interest  which  may  here  be 
neglected.  And  we  may  answer  at  once.  No  result  of  mere 
imagination  can  be  an  inference.  It  can  not  be  a  conclusion, 
because  it  is  not  a  judgment.  The  production  of  imagery 
may  no  doubt  follow  strictly  the  logical  sequence  to  a  certain 
point ;  but  there  it  breaks  off.  For  instance  Kb  may  proceed 
to  a  result  of  fancy  through  logical  functions  b  —  c^  c  —  d;  but 
the  result  when  obtained  is  now  not  integrated  logically  with 
A.  On  the  contrary  it  appears  as  an  individual  image  D, 
and  that  image  is  not  a  predicate  of  A^.  It  certainly  stands 
in  relation  with  Kb^  but  it  falls  into  that  relation  through 
psychical  co-existence  ;  and  so  once  more  we  have  conjunction 
without  connection. 

We  have  no  judgment,  since  the  result  is  mere  fact  which 
exists  in  the  mind,  and  since  it  is  not  a  symbolic  content 
referred  away  from  its  own  existence.  It  exists  and  it  stands 
in  certain  relations,  but  it  is  not  taken  as  an  adjective  which  is 
either  true  or  false.     And  then  the  given  A,  with  which  we 


Chap,  ni.]      GENERAL  CHARACTERISTICS  OF  INFERENCE.      4II 

Started,  does  not  survive  in  the  result  ;  it  does  not  appropriate 
the  content  and  use  it  as  its  attribute.  That  content  breaks 
its  logical  bond,  and,  wandering  off  into  the  psychical  space, 
begets  by  contact  with  beings  external  to  A  an  independent 
substantive  D  ;  which,  itself  autonomous,  has  now  a  substantival 
relation  to  A.  Hence  we  have  no  logical  unity  in  the  object, 
no  ideal  individuation. 

§  24.  Imagination  is  certainly  not  free  from  logical 
processes.  Its  trains,  no  doubt,  throughout  a  great  part  of 
their  length  may  consist  of  the  strictest  intellectual  sequences. 
They  may  contain  few  images,  and  but  little  save  the  purest 
symbolic  ideas.  Yet  somewhere  we  find  a  solution  of  con- 
tinuity ;  somewhere  the  identity  of  the  datwn  is  lost ;  at 
some  point  we  pass  from  the  adjectival  content  attributed  to 
our  basis,  and  slide  into  an  image  which  is  not  its  predicate. 
And  with  this  break,  wherever  it  comes,  we  have  left  judg- 
ment for  fancy,  and  are  not  concerned  with  truth  but  with 
psychical  fact. 

It  would  no  doubt  be  interesting  to  pursue  this  enquiry ; 
but  the  interest  would,  I  think,  in  the  main  not  be  logical.  It 
would  in  the  first  place  be  psychological,  and  then  perhaps 
aesthetic.  But  the  broad  distinction,  that  what  is  merely 
imagined  is  not  held  to  be  true,  removes  imagination  from  the 
province  of  logic.  We  shall  however  be  forced  to  touch  again 
on  this  point  when  we  deal  with  the  early  developement  of 
reasoning  (Chap.  VI L). 

§  25.  Inference  then,  so  far  as  we  have  seen,  is  an  ideal 
experiment  which  procures  a  result  from  a  given  basis.  This 
result  is  a  judgment  in  which  the  new  product  is  predicated 
of  the  given.  And  in  this  whole  operation  we  have  found  that 
identity  which  our  Second  Book  perceived  to  be  essential  to 
the  middle  construction.  But  our  enquiry  so  far  has  stopped 
short  of  the  goal.  We  are  naturally  still  curious  about  this 
middle  process.  We  still  ask  Is  there  not  some  central 
identity  to  be  found  in  this  ?  And  we  shall  take  up  this 
question  in  Chapter  V.  ;  but,  before  we  can  answer  it,  it  is 
necessary  to  inspect  our  types  of  inference  and  to  reduce 
them,  if  we  can,  to  some  more  general  form 


412  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 


CHAPTER  IV. 

THE  MAIN   TYPES   OF   INFERENCE. 

§  I.  In  our  Second  Chapter  we  detailed  a  number  of 
intellectual  processes,  all  claiming  to  be  inferences.  These 
processes  present  us  with  many  varieties  of  that  middle 
operation,  which  we  have  seen  is  one  essential  part  of  reason- 
ing. In  the  present  Chapter  we  are  to  neglect  many- 
questions.  We  are  not,  for  instance,  to  say  anything  about 
the  validity  of  these  processes,  nor  to  attempt  to  reach  their 
ultimate  nature.  We  shall  be  content,  if  we  can  show 
throughout  their  detail  two  or  three  main  types  of  ideal 
experiment. 

There  are  two  general  classes  we  can  at  once  point  out. 
The  operations  we  mentioned  seem  to  fall  under  the  heads 
of  synthetical  construction  and  analytic  elimination.  We  may 
at  least  say  of  these,  that  we  find  no  inference  which  does  not 
contain  one  of  them. 

§  2.  In  that  form  of  reasoning  which  is  most  familiar  we 
verify  the  presence  of  both  these  activities.  Thus  from  A  —  B 
B  —  C  we  go  by  a  synthesis  to  A  —  B  —  C,  and  then  use  elimina- 
tion to  bring  out  A  —  C.  The  preparation  which  precedes  the 
final  intuition,  has  thus  two  aspects.  But  on  the  other  hand 
this  does  not  seem  to  hold  good  with  all  types  of  inference. 
When  for  instance  we  argue  without  elision  to  a  new  quality 
of  the  whole  (as  was  the  case  when  we  discovered  our  island), 
we  seem  to  employ  construction  alone  ;  and  in  abstraction 
again  we  do  not  seem  to  use  construction  at  all.  There  is 
no  apparent  synthesis  when  we  analyze  the  given,  and 
eliding  one  part  then  predicate  the  residue.  Yet  this  is  not 
the  point  we  are  at  present  concerned  with.  To  ask  whether, 
and  in  what  sense,  the  isolated  employment  of  one  function 
is    possible,  would   here   be    premature,   and  at  present   we 


Chap.  IV.]  THE   MAIN   TYPES   OF  INFERENCE.  413 

may  be  satisfied  if  one  of  these  processes  can  be  dis- 
covered everywhere.  We  shall  proceed  to  assign  our  list  of 
operations  each  to  one  head,  but  must  not  be  understood  to 
exclude  it  from  the  other.  Thus  we  shall  call  an  inference 
synthesis  or  analysis,  according  as  each  type  appears  more 
prominent  in  each  case. 

§  3.  (A)  Let  us  begin  with  cotistruction  and  see  what 
processes  will  fall  naturally  under  this.  (i)  Those  syntheses 
of  relations  which  group  themselves  round  an  identical  centre, 
will  take  the  first  place.  Whether  they  end  in  a  new  internal 
relation,  or  remain  joined  in  one  whole,  or  proceed  to  a  new 
quality,  in  each  case  their  most  prominent  aspect  is  synthesis. 
The  first  class  of  constructions  are  those  which  are  based  on 
an  explicit  identity,  which  so  to  speak  forces  the  extremes 
together. 

As  compared  with  these  all  the  rest  seem  arbitrary.  For 
we  have  in  none  the  bond  of  a  given  centre,  while  in  some  it 
is  doubtful  if  any  kind  of  centre  exists.  The  ideal  unity  is 
not  anywhere  prescribed  to  us  beforehand.  In  some  cases 
it  looks  as  if  the  operation  were  capricious ;  and  it  is  a 
question,  to  which  we  must  hereafter  return,  how  far  the  con- 
clusion can  stand  either  with  or  without  this  operation.  Since 
at  present  these  constructions  seem  not  necessary,  like  the 
first,  since  their  middle  term,  if  they  have  one,  appears  our 
mere  choice,  we  may  distinguish  them  here  as  arbitrary  syn- 
theses. 

§  4.  As  such  (ii)  we  recognize  addition  in  Arithmetic,  and 
the  geometrical  extension  of  figures.  In  each,  under  differ- 
ences, we  find  the  same  process  of  free  rearrangement.  I 
obtain  a  result  by  composition  of  elements,  and  that  result  is 
held  true  of  the  elements  themselves.  The  same  holds  with 
Comparison.  There  I  bring  the  terms  together,  I  unite  them 
under  a  certain  aspect,  and  I  then  see  a  quality  which  I  pro- 
ceed at  once  to  predicate  of  these,  terms.  In  the  process  of 
Recognition  I  may  seem  less  at  liberty,  and  still  less  free  in 
Dialectic  reasoning  :  but  in  both  cases  the  main  feature  is  the 
construction  of  a  whole — a  construction  round  a  centre,  which 
is  not  given,  into  an  unity  not  prescribed  by  the  premises. 

§  5.  Our  material  so  far  has  arranged  itself  under  the  head 


414  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

of  Construction  ;  and  the  synthesis  seemed  in  some  cases  to 
be  necessary  and  in  others  arbitrary.  We  pass  next  to  the 
consideration  of  that  other  main  type  which  is  the  counterpart 
of  the  first. 

(B)  The  essence  of  analysis  consists  in  the  division  of  a 
given  totality,  and  in  the  predication  of  either  the  whole  or 
part  of  the  discrete  result.  In  the  latter  case  the  presence  of 
Elision  is  manifest,  but  even  in  the  former  it  is  to  be  recog- 
nized. When  reality  first  appears  as  a  whole  and  then  as  a 
number  of  divided  units,  something  certainly  is  gained  but 
something  else  is  eliminated.  For  the  aspect  of  continuity  or 
unity  is  left  out ;  and  thus  mere  analysis  always  involves  and 
must  involve  some  elision. 

The  first  example  of  this  class  may  be  found  in  Abstrac- 
tion. We  are  burnt,  and  proceed  from  this  experience  to  the 
result,  Fire  burns.  We  have  first  reality  as  giving  the  whole 
complex,  we  have  next  the  elimination  of  all  content,  save  two 
elements  in  connection,  we  have  thirdly  the  predication  of  this 
residue  ;  Fire  burning  is  real.  The  validity  of  the  process  is 
open  to  grave  doubt,  but  it  consists  in  analysis  followed  by 
elision. 

Arithmetical  subtraction  shows  the  same  features.  Reality 
gives  us  an  integer  five.  We  then  divide  this  into  units,  and, 
removing  two  of  them,  get  an  integer  three,  which  we  predi- 
cate of  reality.  And  we  assume  here  once  more  that  the 
units  are  not  altered  by  the  disruption  of  their  context.  This 
assumption  may  be  false,  but  the  process  is  clearly  one  of 
elision. 

In  Distinction  we  seem  to  have  a  new  variety,  but  we  still 
may  find  the  same  general  outline.  We  are  presented  with 
elements  which  are  taken  as  one.  Altogether,  or  with  refer- 
ence to  a  part  of  their  content,  they  come  before  us  as  a  whole, 
obscure  no  doubt  but  still  unbroken.  In  the  result  of  the 
operation  this  whole  has  vanished.  A  and  B  fall  apart  and 
appear  as  divided,  entirely  or  in  respect  of  one  or  more  attri- 
butes ;  and  then  this  result  is  attributed  to  the  original  reality. 
We  shall  once  more  neglect  the  suspicion  which  such  an 
assumption  excites.  Confining  ourselves  to  the  general 
character  of  the  operation  employed,  we  are  able  again  to 


Chap.  IV.]  THE   MAIN   TYPES   OF   INFERENCE.  415 

verify   our   type.      A   totality   is    divided   by   a  function    of 
analysis,  and  ignored  in  the  product  by  an  act  of  elimination. 

§  6.  We  have  seen  so  far  that  all  our  examples  fall  under 
two  heads.  Can  we  advance  to  the  conclusion  that  inference 
consists  in  two  main  processes,  construction  and  elision  ?  Our 
way  is  barred  by  an  unforeseen  obstacle  ;  for  we  have  not  yet 
dealt  with  Disjunctive  reasoning.  And  it  is  impossible  to 
reduce  this  wholly  to  either  process  or  to  a  mixture  of  both. 
Both  indeed  are  concerned  in  it,  but  they  do  not  exhaust  it. 

If  the  alternatives  are  given  us  with  an  explicit  statement 
of  their  reciprocal  exclusion,  and  of  the  sequence  of  each  from 
the  absence  of  the  other,  in  that  case  we  do  not  find  a  new 
principle  of  reasoning.  For  one  of  our  data  removes  a  pos- 
sibility, and  that  removal  does,  by  virtue  of  another  datum, 
assert  the  remaining  possibility  as  fact.  In  ''  A\s  b  or  c  "  and 
"  A  is  not-^,"  by  combining  our  premises  we  bring  in  not-^, 
and  so  banish  c  ;  and,  this  affirmation  of  not-^  being  elided, 
we  can  then  join  b  directly  to  A.  Thus  where  the  "or"  is 
explicit,  we  have  nothing  which  falls  outside  our  two  principles. 

But  suppose  we  start  with  possibilities  not  given  as  strict 
alternatives.  If,  for  instance,  A  may  be  b,  and  again  may  be 
c,  and  can  be  nothing  else  ;  and  if  we  further  suppose  that  A 
is  not  c,  what  conclusion  can  we  draw  ?  Can  we  go  to  There- 
fo7'e  A  must  be  b  ?  We  do  indeed  make  this  advance,  but  the 
advance  is  made  on  the  strength  of  the  fresh  assumption  that 
any  unopposed  possibility  is  real.  And  this  means  a  new 
principle.  For  here  what  we  predicate  is  not  the  residue  of 
truth,  but  the  remainder  of  chance.  We  attribute  to  the  real, 
not  something  first  given  and  then  worked  upon  by  our  act, 
but  an  issue  from  premises  which  afford  nothing  positive.  We 
do  not  go  simply  from  the  mutilation  of  a  whole  to  the  accept- 
ance of  a  part,  but  we  also  leap  from  the  possibility  of  that  part 
to  its  unconditional  existence.  This  principle,  which  we  before 
had  need  to  mention  (Chap.  II.  §  26),  and  which  will  engage 
us  hereafter,  will  not  fall  under  the  head  of  either  analysis  or 
synthesis. 

§  7.  Disjunctive  reasoning  may  employ  all  three  processes, 
but  it  certainly  need  not  do  this.  Where  alternatives  are 
explicit,  we  have  seen  that  it  is  content  with  the  use  of  two. 


4l6  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

And  there  is  another  instance  where  two  are  enough.  For 
where  the  process  is  ponendo  tollens — where  from  "  A  may  be  b, 
and  A  may  be  c  (though  not  both),  but  A  is  c"  we  advance  on 
the«strength  of  an  ideal  synthesis  to  "  A  excludes  b  " — we  are 
not  forced  to  cross  from  the  possible  to  the  actual.  We 
remain  in  the  latter,  and  the  exclusion  of  the  possible  is,  as 
such,  no  real  quality  of  A  (vid.  Book  I.  Chap.  III.). 

But  in  other  cases  three  movements  may  be  seen.  The 
argument  constructs  and  then  eliminates  ;  and  in  the  end  the 
residue  is  predicated  with  a  vital  change  in  its  character. 
Under  this  general  type,  which  calls  in  the  third  movement, 
we  may  point  out  several  varieties. 

In  the  first  of  these  (§  6)  the  possibilities  are  given,  not  as 
explicit  alternatives,  and  yet  as  together  exhausting  the  subject ; 
and  also  along  with  these  possibilities  may  be  given  the  actual 
exclusion  of  one.  This  is  the  first  variety.  In  another  we 
are  left  to  make  a  complete  exhaustion  for  ourselves  ;  and 
again  in  another  we  may  have  no  possibilities  given  us,  and 
may  even  have  no  statement  of  exclusion.  In  this  last  ex- 
treme case  we  are  reduced  to  operate  with  mere  suggestions. 
Thus  if  on  trial  b  is  found  possible,  and  A  excludes  the  sug- 
gested c,  d,  and  e,  and  if  in  the  end  we  can  find  nothing  else  which 
we  are  able  to  suggest — then  we  advance  to  the  conclusion,  A 
must  be  b.  We  have  conjoined  b  with  A,  have  eliminated  the 
rest,  and  have  boldly  leapt  from  "  may  be  "  to  "  must  be." 
Here  the  exhaustion  was  not  guaranteed,  nor  the  exclusion 
given.  Our  datum  was  A  ;  and  it  was  we  ourselves  who  con- 
structed the  whole,  assumed  its  completeness,  elided  one  part, 
and  then  sprang  to  the  actuality  of  our  product. 

In  all  these  latter  varieties  of  disjunctive  reasoning,  we 
have  first  synthesis  and  then  elimination,  the  whole  con- 
summated thirdly  by  a  transition  to  fact  from  mere  possibility. 

§  8.  In  this  last  section  we  have  already  provided  for  Apa- 
gogic  inferences  (Chap.  II.  §  29),  and  have  finished  our  rapid 
survey  of  the  principal  classes  of  reasoning.  We  may  now  pre- 
sent the  result  in  a  tabular  form,  asking  the  reader  to  bear  in 
mind  one  thing.  He  must  remember  that,  when  a  process  is 
referred  to  one  head,  he  is  not  to  assume  that  the  other  type  is 
absent.    We  are  to  class  each  operation  by  its  more  prominent 


Chap.  IV.]  THE   MAIN   TYPES   OF   INFERENCE.  417 

feature,  and  to  neglect  for  the  moment  our  additional  step 
from  the  possible  to  the  actual. 


A. 

Constrtiction. 

(i) 

Where  the  whole  is  madel 

(a)  necessarily.^ 

out  of  the  datum                | 

(/3)  arbitrarily.^ 

(ii; 

)  Where  the  whole  is  made) 

(a)  necessarily.^ 

beyond  the  datum              \ 

(/3)  arbitrarily.* 

B. 

Eliminative  analysis. 

Where,  the  whole  being  given, 

1     {a)  necessary.^ 

the  elision  is 

1     (/3)  arbitrary.^ 

We  may  enumerate  the  processes  here  presented.  We 
have  in  No.  i  the  three-term  inference  which  we  first  discussed. 
In  No.  2  we  find  addition  and  comparison.  No.  3  gives  us 
recognition  and  dialectic  movement.  With  No.  4  we  reach 
determination  (positive  or  negative)  by  means  of  a  suggested 
possible  synthesis.  Thence  we  come  in  No.  5  to  that  dis- 
junctive reasoning  where  the  possibilities  are  independent  and 
one  is  excluded.  Then  No.  6  closes  the  rear  with  abstraction, 
distinction,  and  arithmetical  subtraction. 

We  may  append  three  remarks.  The  first  of  these  is  that 
the  Hypothetic  judgment  may  be  assigned  to  No.  3.  It  may 
be  said,  no  doubt,  that  we  are  at  liberty  not  to  suppose ;  but 
then  on  the  other  hand  we  also  elsewhere  are  free  not  to  think. 
The  premise  is  a  datum  not  given  as  real ;  I  treat  it  logically, 
and  thus  get  a  result  which  I  conditionally  predicate.  But 
nothing  here  is  my  choice,  save  the  resolve  to  suppose  and 
then  to  see  what  logically  comes.  But  so  much  choice  as  this 
seems  to  exist  in  all  reasoning,  since  everywhere  it  lies  with 
ourselves  at  least  to  think  or  not  to  think. 

In  the  second  place  addition  and  subtraction  will  be 
necessary  where  the  quantities  are  given  marked  with  plus  or 
miftus.  But  their  result  in  this  case  is  hypothetical.  The 
signs  do  not  belong  to  the  nature  of  the  quantities  (Chap.  II. 
§§6  and  10).  And  the  reader  must  remember  that  free 
spatial  rearrangement  falls  under  the  heads  of  2  and  6. 

And  the  third  remark  we  have  to  make  is  this.  The 
process  of  suggesting  possible  predicates,  and  of  then  proving 
one  by  excluding  the  others,  may  be  regarded  as  a  mixture 

2  E 


41 8  THE   PTIINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

of  Nos.  4  and  5  ;  but  it  is  not  worth  while  to  place  it  in  a  class 
by  itself. 

We  may  end  by  stating  briefly  the  conclusion  of  this 
Chapter.  The  middle  operation  of  every  inference  consists  of 
analysis  or  synthesis,  or  both  ;  and  in  certain  cases  it  invokes 
besides  an  additional  principle. 


(  4i9  ) 


CHAPTER  V. 

ANOTHER  FEATURE  OF  INFERENCE. 

§  I.  We  must  search  into  the  nature  of  these  general 
processes,  but  there  is  a  question  which  presses  for  immediate 
answer  in  the  present  Chapter.  We  supposed  first  of  all  that 
every  inference  was  a  construction  round  an  identical  centre. 
We  have  since  then  discovered  that  reasoning  demands  a 
self-same  subject,  that  appropriates  the  difference  got  by  the 
experiment.  But  we  must  return  to  examine  the  middle 
operation,  the  experiment  itself.  We  now  know  that  our  first 
supposition  needs  correction,  since  the  experiment  is  not 
always  a  construction  through  a  given  "identity.  But  this 
result  does  not  satisfy  us.  We  want  to  know  if  our  middle 
process  can  ever  dispense  with  all  identity.  There  clearly  is 
not  always  an  explicit  common  term  ;  and  when  this  fails  shall 
we  say  that  everything  has  failed  1  Or  can  we  still  say,  there 
is  an  implicit  centre,  unavowed  but  active  .?  Our  instinct  leads 
us  to  embrace  this  latter  suggestion. 

§  2.  But  how  shall  we  support  it }  There  is  obviously 
some  unity  in  the  operation,  but  it  is  doubtful  if  this  will  give 
us  what  we  want.  Mere  togetherness  (so  to  speak)  before  the 
mind  is  clearly  insufficient ;  and  we  must  hence  take  the  mind 
itself  as  a  centre,  not  given  but  used,  and  see  if  on  this  line  we 
can  make  an  advance.  We  may  say,  "  In  all  relations,  where 
the  terms  are  able  to  be  separated  in  idea,  the  relation  may  be 
considered  as  an  interrelation.  The  result  is  an  inference,  a 
putting  together  of  elements  which  before  that  inference 
existed  apart.  And  since  those  elements  were  all  related  to 
one  mind,  and  because  of  that  unity  now  come  together,  the 
mind  may  be  taken  as  a  common  centre  of  interrelation."  Is 
this  what  we  want }  We  must  answer  in  the  negative ;  for 
though  I  believe  it  to  be  true,  and  a  truth  whose  importance 

2  E  2 


420  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

can  hardly  be  exaggerated,  yet  in  its  abstract  form  it  is  simply 
irrelevant.  It  tells  us  that  some  relation  of  some  kind  exists 
between  all  objects  of  thought,  and  that  they  are  all  interre- 
lated. But  then  this  knowledge  must  fall  outside  of  any 
special  inference.  Thus  A  and  B  are  called  equal  because  I 
have  compared  them  ;  but,  before  I  compared  them,  I  might 
have  known  that  some  relation  must  exist  between  them  ;  and 
this  knowledge  is  therefore  not  the  reason  why  I  now  know 
that  they  are  equal. 

§  3.  From  mere  interrelation  you  can  make  no  passage  to 
a  special  relation.  It  does  not  matter  how  actively  the  mind 
may  work ;  you  may  suppose  an  intense  appreciation  of  the 
fact  that  we  have  a  common  term  in  the  mind  ;  you  may 
postulate  any  degree  of  attention,  or  the  preferential  application 
of  the  intellect  to  this  fact — yet  from  these  general  premises 
you  never  will  get  to  the  particular  conclusion.  For  the 
centre  of  the  operation,  if  we  are  to  find  it  at  all,  must  be 
found  in  the  unity  of  that  special  operation.  We  can  not 
settle  such  a  point  by  abstract  reflections,  which  at  the  most 
serve  to  raise  a  vague  presumption  in  our  favour.  If  we 
wish  to  exhibit  the  identity  in  our  processes,  we  must  be 
prepared  to  show  the  central  point  in  each  particular  case. 

§  4.  Let  us  start  with  what  we  called  Recognition  and 
Dialectic.  The  given  here  is  A7,  and  the  mind  meets  this 
with  a  function  7-8,  which  extends  A  to  8.  The  central  point 
is  here  obviously  7 ;  and  round  this  point,  and  by  virtue  of  its 
identity,  A  and  8  are  brought  together.  We  must  notice  how- 
ever that  7-S  is  not  given,  and  further  that  7-S  may  never  be 
explicit.  Our  consciousness  may  pass  straight  from  A7  to  h. 
It  may  never  suspect  the  presence  of  that  common  middle 
term  on  which  everything  depends.  Hence  we  might  say 
that  we  have  subsumed  the  original  datum  under  a  function  of 
synthesis,  which  never  appears  except  in  its  effects  :  but  this 
statement  would  be  incorrect,  since  the  process  is  not  a 
subsumption  at  all.  It  is  a  construction  by  means  of  a  hidden 
centre. 

This  seems  tolerably  clear,  and  it  gives  us  a  principle  to 
which  we  must  hold.  But  in  its  further  application  the  truth 
becomes  much  more  difficult  to  see. 


Chap.  V.]  ANOTHER   FEATURE   OF   INFERENCE.  42 1 

§  5.  If  we  consider  the  operations  of  Comparison  and 
Distinction,  we  are  at  first  unable  to  perceive  any  middle. 
The  mind,  we  may  say,  is  the  point  which  compares,  and  the 
centre  which  separates  ;  but  such  a  mere  generality,  however 
important,  we  agreed  was  not  the  answer  that  is  wanted. 
The  question  is  whether  in  the  process  itself  we  can  find  a 
special  interrelation ;  and  we  shall  now  make  this  attempt. 

Both  the  processes  exhibit  a  double  aspect  of  unity  and 
diversity.  In  Comparison  this  fact  is  at  once  apparent.  Irv 
"A  =  B"  we  have  of  course  the  differences  of  A  and  B. 
These  differences  are  held  together  in  relation,  and  are 
combined  on  the  strength  of  a  common  point,  since  the 
quantity  of  A  and  B  is  the  same.  Thus  the  relation  of  each 
difference,  A  and  B,  to  an  identical  quantity  is  the  very 
ground  of  their  interrelation.  Take  that  third  term  away,  and 
the  connection  vanishes  ;  reproduce  it,  and  the  mind  requires 
nothing  else  in  order  once  more  to  construct  the  relation. 

But  is  it  so  too  with  Distinction  }  Take  for  instance,  "  A 
is  not  equal  to  B,"  and  where  is  the  third  term  }  I  answer.  It 
is  there,  though  we  do  not  perceive  it  For  consider  the  case 
thus  ;  A  and  B,  it  is  certain,  are  still  related,  since  they  are 
taken  as  different ;  and  their  difference  is  not  abstract  but 
specific  and  definite.  It  is  as  quantities  that  we  fail  to  find 
them  identical.  But,  this  being  grasped,  observe  what  follows. 
Just  as  the  general  perception  of  difference  implies  a  mind 
which  distinguishes,  and  which  serves  in  some  vague  character 
as  the  base  which  supports  that  general  relation — so  it  is  with 
every  special  difference.  What  is  true  in  general  will  prove 
true  in  particular.  All  objects  of  our  thought  in  the  first 
place  must  have  so7ne  relation  because,  as  our  objects,  they  are 
all  identical ;  and  again  every  distinction  of  special  qualities, 
such  as  sounds  or  colours,  takes  place  on  the  basis  of  a 
special  community.  For  instance,  the  separation  of  red  from 
blue  must  imply  the  unconscious  taking  of  each  as  a  colour  ; 
and  that  felt  common  quality  is  the  basis  upon  which  the 
separation  is  effected.  It  is  thus  too  with  quantities.  A  and 
B  are  perceived  to  be  unequal,  but  inequality  presupposes 
that  both  have  quantity.  In  this  they  are  the  same^  and  it  is 
because  of  this  point  that  they  can  be  seen  as  unequal.     Thus 


422  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  1. 

identity  in  regard  to  the  possession  of  quantity  is  here  the 
third  term  that  was  required,  and  it  is  relation  to  this  centre 
which  interrelates  the  quantitative  differences.  In  short 
distinction  can  never  be  effected  except  within  an  area  of 
sameness ;  and,  once  outside  this  area  and  common  meeting- 
ground,  the  relation  would  vanish. 

§  6.  Perception  of  identity  and  perception  of  difference 
are  two  modes  of  one  function  or  two  functions  of  one  process. 
The  result  in  both  cases  depends  on  a  synthesis  of  diversity 
with  unity,  but  with  this  likeness  there  goes  a  striking 
contrast.  Take  first  Comparison.  Here  we  start  with  the 
difference,  and  at  the  end  this  difference  has  been  partially 
lost,  and  the  identity  of  the  terms  has  become  explicit.  It 
is  otherwise  with  Distinction.  We  begin  here  with  a  vague 
and  undiscriminated  unity,  but  in  the  conclusion  the  differences 
appear,  and  the  identity  has  passed  away  from  our  sight.  In 
both  processes  alike  the  sameness  of  the  terms  is  the  middle 
point  from  which  everything  hangs  ;  but  that  centre  is  used  in 
two  diverse  ways.  In  the  case  of  Comparison  it  is  the  recep- 
tive identity  which,  standing  opposite  to  external  differences, 
takes  them  into  itself  Content  with  a  partial  recognition 
of  its  power,  satisfied  with  a  declaration  made  by  the 
differents  that  in  some  point  they  are  the  same,  the  unity 
slurs  the  remainder  of  diversity,  and  becomes  the  mere 
relation  of  similars.  But  the  process  of  Distinction  shows  a 
contrast  to  this.  The  identity  here  turns  against  its  own 
unseen  differences,  and  makes  them  explicit.  It  pronounces 
the  relation  which  sunders  them  apart,  and  is  led,  by  the 
emphasis  of  this  its  own  activity,  to  forget  its  own  being- 
Thus  the  differents  appear  as  independent  varieties,  which 
subsist  and  form  relations  in  a  passive  atmosphere.  The 
identity  which  has  generated  them,  which  separates  and 
supports  them,  is  slurred  even  more  than  in  the  former  case 
diversity  was  slurred  by  Comparison.  We  might  say  that  one 
tends  to  think  less  of  the  relatives  and  more  of  the  relation  ; 
while  the  other  quite  sinks  the  active  ^relation,  and  keeps  its 
eye  on  the  terms  related. 

§  7.  In  the  ensuing  Chapter  we  shall  return  to  this  point 
but   at   present  we    may  try  to   develope  our  meaning.  /  In 


Chap.  V.]  ANOTHER   FEATURE   OF   INFERENCE.  423 

Comparison  and  in  Distinction  we  employ  certain  functions, 
and  you  might  say  incorrectly  that  these  processes  consist  in 
subsuming  the  given  under  certain  activities.  What  are  these 
activities  ?  In  a  clumsy  fashion  we  may  represent  them  as 
follows.     In    Comparison   we   apply   to   the   original   datum, 

X 
A   and   B,    a   function   of  synthesis,    /\ .     Through   the 

a        b 
possession  by  A  and  B  of  the  qualities  a  and  b,  we  unite  them  in 
relation  to  our  common  point  X.     The  result  may  be  depicted 

X 

as      X\     ;  but,  since  the  unity^  is   degraded  and  becomes  a 

A       B 
relation,  the  conclusion  which  appears  is  simply  A  —  B. 

For  Distinction  we  must  bring  in  another  formula.     We 
may  be  said  to  start  with  a  vague  totality,  in  which  is  latent 
an  internal   diversity  ;  and  we  may  represent  this  datum  as 
X  X 

/\    .     To  this  unity  we  apply  a  function  of  analysis    /\    . 
a        b  A       B 

Then  on  the  one  hand  X,  now  identified  with  x,  becomes  less 
visible ;  while,  as  this  fades  away,  the  other  side  appears,  and 
a  and  b,  developed  by  the  application  of  the  function,  appear 

X 

as  A  and  B.     The  immediate  result  is    /\    ,  but,  since  x  is 

A       B 
wholly  slurred,  A  and  B  fall  apart  as  separate  facts  which 
show  a  distinction. 

§  8.  It  would  be  interesting  to  enter  into  the  finer  meta- 
physical detail  of  these  processes  ;  but  we  can  afford  no 
more  than  a  mere  passing  remark  in  protest  against  an 
obstinate  prejudice.  In  answer  to  the  doctrine  that  sameness 
and  diversity  imply  one  another,  at  least  when  perceived,  we 
shall  be  told  that  Difference  is  independent,  and  derives  its 
origin  from  the  shock  of  change.  And  for  the  apprehension 
of  this  shock,  it  will  be  added,  no  activity  is  required.  Thus 
we  have  no  ideal  operation  at  all,  and  may  so  dispense 
with  the  illusion  of  an  ideal  unity."  But  this  objection,  I 
must  reply,  depends  upon  a  complete  mistake.  It  partly 
confuses     feeling    with    perception,    and     partly    is    wholly 


424  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

wrong  about  feeling.  I  will  take  the  second  of  these  points 
first. 

If  a  shock  is  intended  to  be  felt  as  a  shock  (and  I  suppose 
it  must  be  so  intended),  then  the  feeling  must  be  compound. 
There  must  be  some  feeling  to  start  with,  in  collision  with 
which  the  inrush  of  new  feeling  disturbs  the  mind.  For  if  the 
place  were  quite  empty  the  new  arrival  might  appear,  but 
could  hardly  make  a  striking  sensation.  Thus  the  shock 
presupposes  another  element,  and  it  implies  the  felt  relation 
of  both.  But,  if  so,  once  more  we  have  found  in  this  relation 
a  point  of  identity,  a  common  sameness  not  of  perception 
but  of  feeling.  In  other  words  it  will  be  the  continuity  of  the 
feeling  which  makes  us  sensible  of  the  change  and  the  shock  ; 
and  this  is  our  first  point. 

But  we  have  not  yet  reached  the  perception  of  change,  and 
the  failure  to  see  this  is  the  second  point  of  error.  Think 
what  you  like  about  the  felt  shock,  you  are  yet  a  long  way 
from  the  consciousness  of  difference,  and  you  can  not  advance 
without  calling  in  an  ideal  identity.  Take  a  sensation  A,  and 
let  it  change  to  a  wholly  different  C.  This  will  give  you  the 
succession  of  two  psychical  events,  but  not  the  perceived 
relation  of  change,  and  the  question  is  how  this  relation  can 
be  given.  It  can  not  be  given  without  retention,  and  retention 
is  not  possible  unless  what  precedes  and  what  follows  possess 
some  point  in  common.  But  let  AB  (for  example)  be  followed 
by  BC,  and  the  problem  is  solved.  Here  the  identical  B 
redintegrates  A  ;  or  (if  you  prefer  to  say  so)  the  retention  of 
AB  gives  us  A  with  a  point  in  common  with  C  ;  and,  in  either 

B 
case,  we  have  a  result  which  we  may  write  /\    .     No  change 

A       C 
can  be  perceived  unless  by  means  of  an  ideal  continuity. 

§  9.  This  ideal  identity  is  a  necessary  element  in  the 
perception  of  difference.  Without  such  a  centre  the  extremes 
would  never  be  held  together,  and  their  relation  would  never 
come  before  the   mind.     We   may  represent   as    follows   the 

A  . 

mode  in  which  this   unity  operates.      In  a  whole   ,    ,,  as  it 

passes   before   us,  the    difference  be  is  not   at   first    noticed. 


Chap.  V.]  ANOTHER   FEATURE   OF  INFERENCE.  425 

Hence  we  do  not  perceive  b  and  c  to  be  disparate,  till  we  try- 
to  identify  them.  But,  in  going  from  Kb  on  to  A^,  the 
self-same  A  reproduces  b,  which,  thus  forced  upon  us  in 
identity  with  ^,  is  rejected  by  it ;  and  then,  A  retiring  from 
view,  we  perceive  the  difference  as  B  against  C. 

How  then  do  we  become  aware  of  identity }  We  must 
have  differences  B^  and  D^,  and  we  must  feel,  when  we  pass 
from  one  to  the  other,  that  they  are  not  all  different.  This 
feeling  comes  from  the  presence  of  a^  which  is  not  yet 
explicit.  It  rises  to  explicitness,  through  the  reproduction  of 
B,  and  the  consequent  collision  of  B  with  D.  By  means  of 
the  alternate  rejection  of  these  discrepants,  the  common 
identity  a  is  set  free  ;  and  the  relation  of  similarity  between 
B  and  D  is  brought  clearly  before  the  mind.  We  may  be  said 
to  begin  with  an  implicit  sameness,  then,  by  working  with  that, 
to  make  our  implicit  difference  visible,  and  from  this  visible 
difference  to  return  back  to  sameness,  bringing  out  in  our 
movement  a  relation  of  similarity,  and  perhaps  in  addition  a 
seen  and  explicit  point  of  identity. 

We  can  not  further  pursue  these  enquiries.  For  our 
object  is  attained  if  we  have  succeeded  in  showing  that,  alike 
in  Distinction  and  in  Comparison,  we  obtain  our  result  by  an 
active  centre  which  stands  in  relation  with  both  the  extremes. 

§  10.  After  leaving  the  perceptions  of  sameness  and 
difference,  we  come  next  to  the  processes  which  depend 
on  these  perceptions.  There  are  a  number  of  remaining 
inferences  which  consist  in  re-arrangement,  in  the  new  group- 
ing of  elements  within  a  whole.  And  here  we  may  make 
a  broad  distinction.  If  our  fresh  distribution  starts  from 
analysis,  then  the  process  falls  throughout  within  that  whole 
which  is  given  us  at  the  start,  and  this  whole  will  be  the 
unity,  relation  to  which  interrelates  the  elements.  But  if  on 
the  other  hand  our  re-arrangement  demands  a  construction 
outside  the  original  datiini — if,  that  is,  we  must  first  extend 
what  is  given  by  addition  of  fresh  elements,  before  we  are 
able  to  find  our  conclusion — in  this  case  our  datiim  is  not  the 
whole  required.  The  entire  ultimate  construction  implies  a 
fixed  ideal  centre  of  its  own,  and  the  extension  and  re-arrange- 
ment will  therefore  take  place  within  a  whole  which  includes 


426  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

our  datum,  a  whole  which,  though  invisible,  still  is  active.    We 
must  apply  this  general  truth  to  our  detail. 

§  II.  If  we  consider  the  free  construction  of  elements  in 
space,  we  find  at  once  that  this  movement  implies  a  centre  of 
identity.  Unless  the  extended  parts  that  we  deal  with  came 
into  one  whole,  our  process  would  be  nugatory.  We  should 
begin  and  end  with  mere  isolated  fragments,  indifferent  to 
each  other,  neither  united  nor  yet  sundered  by  spatial  relations. 
Our  conclusion  implies  that  the  elements,  we  begin  with,  are 
members  of  one  space.  But,  if  they  belong  to  one  extended 
whole,  they  either  must  have  identical  points,  or  must  all  be 
connected  with  some  common  centre.  So  much  is  clear,  and 
will  perhaps  be  admitted.  On  the  other  hand  a  serious  dif- 
ference of  opinion  would  at  once  arise,  if  we  asked  where  the 
middle  of  space  can  be  found.  Is  all  motion  merely  relative  } 
Is  there  again  an  actual  existing  centre  by  which  all  else 
is  determined  }  Or  is  not  this  point  of  reference  merely  ideal, 
something  that  does  not  and  indeed  that  can  not  exist }  But 
we  need  not  answer  these  questions  here.  It  is  enough  if  we 
agree  that  all  spatial  grouping,  perceived  or  imagined,  implies 
some  kind  of  common  focus,  whether*  that  focus  be  before  us 
explicitly,  or  whether  it  be  a  mere  unconscious  implication. 
But,  if  so,  it  is  clear  that  our  new  relation  springs  from  inter- 
relation, and  depends  upon  a  point  of  identity. 

§  12.  And  the  same  thing  holds  when  we  come  to 
Arithmetic.  When  an  integer  is  divided  the  analysis  takes 
place  within  the  limits  of  that  unity,  and  the  elements  are 
separated  from  that  centre  of  dispersion.  The  point  of  inter- 
relation no  doubt  disappears  in  the  product  which  we  see.  It 
becomes  invisible  ;  but  if  you  removed  it  wholly,  you  would 
find  that  your  discrete  units  had  vanished.  They  would  in 
this  case  have  lost  the  common  relation  which  keeps  them 
apart,  and  gives  them  their  show  of  independence.  But  just 
as  here  continuity  is  active  in  the  production  of  discretion,  so 
again,  when  the  discrete  returns  once  more  to  explicit  oneness, 
an  implicit  continuum  is  presupposed.  If  the  units  had  no 
relation  to  a  common  centre,  they  never  could  be  added.  Let 
us  consider  this  last  statement. 
^  Even  if  we  adopt   an  erroneous   view,  the  truth   of  our 


Chap.  V.]  ANOTHER   FEATURE  OF  INFERENCE.  427 

statement  will  still  be  plain.  Let  us  suppose  that  the  units 
have  no  relation  amongst  themselves,  but  are  simply  pushed 
together  by  the  action  of  the  mind,  or  fall  together  in  the 
mental  space.  But,  in  the  latter  case,  how  could  they  all  fall 
towards  one  point,  if  they  were  not  co-partners  of  one  spatial 
world?  And  how  once  more  could  that  world  be  single, 
if  it  had  not  got  some  kind  of  centre  .?  And,  in  the  former 
case,  where  we  suppose  that  the  mind  is  an  external  agent 
which  forces  the  unity,  it  surely  could  not  act  upon  all  the 
units  unless  each  single  unit  were  related  to  this  one  operator. 
Nor  again  would  this  one  special  operation  be  performed,  were 
it  not  that  the  agent  stood  in  one  special  attitude  to  all  the 
pieces  of  material.  So  that,  even  if  we  accept  such  mistaken 
views  about  addition,  we  are  still  compelled  to  believe  in  an 
interrelation. 

But  in  reality  the  units  are  not  independent,  nor  need  we 
invoke  external  violence  to  crush  them  together.  For  they 
arise  and  they  consist  in  the  suppression  of  an  integer,  and 
would  not  be  many  if  they  were  not  thus  one.  Their  relation 
to  each  other  is  the  degraded  form  in  which  their  ideal  con- 
tinuity is  manifest ;  and, '  when  w^e  think  out  this  onesided 
appearance,  we  are  forced  to  advance.  The  discretion  of  the 
units  implies  a  connection  of  each  with  an  unseen  centre  of 
repulsion  ;  but  that  means  on  the  other  hand  their  common 
interrelation  by  virtue  of  this  unity,  which  so  reappears  as  the 
integral  whole  in  which  they  subsist.  We  can  see  this  even 
when  we  take  at  haphazard  a  number  of  units  and  increase  it 
at  our  pleasure.  I  will  not  ask  hoiv  we  are  able  to  do  this, 
though  the  answer  to  that  question  might  help  us  forward. 
Suppose  that  somehow  the  new  unit  is  got.  Yet,  before  it  is 
added,  it  must  have  a  relation  to  the  units  that  exist ;  and  this 
relation  implies  a  common  world  of  number,  and  a  central 
point.  If  this  were  not  present  the  mind  could  not  add  ;  and 
therefore  the  addition  makes  explicit  an  ideal  unity  which  was 
active  though  latent.  It  is  on  the  strength  of  this  idea  that 
the  mind  can  work  and  can  make  the  idea  visible.  Con- 
tinuity is  no  ghost,  that  is  laid  in  the  units  and  conjured  up  to 
surprise  us  in  the  integer ;  it  is  the  soul  which  unseen  is  felt 
in  the  limbs,  and  returns  to  the  centre  with  a  fuller  life. 


428  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

§  13.  Abstraction  is  the  process  which  next  claims  our 
attention.  It  first  involves  a  function  of  analysis.  In  A  we 
distinguish  b,  c,  and  d,  and  we  may  say  that  we  start  from  a 

X 

datum  xA  and  then  proceed   to  a   result  /|\  .     This,  we 

b—c—d 
know  already,  has  been  got  by  means  of  an  identical  centre 
and   still   implies   it,   for   the    unity  A   has   been   sunk   but 
survives. 

Let  us  proceed  to  the  next  step.  We  take  b-c-d,  and  re- 
arrange these  elements,  and  so  get,  by  fresh  grouping,  b-c  on 
one  hand  and  d  on  the  other ;  thus,  b-c  \  d.     Now  identify 

X 

the  b-c  and  the  d  in  /|\    with   the  last-gained   result,    and 

b — c — d   /b — c 
we  reach  the  conclusion  X\^  ,  where  each  relation  to  x 

seems  independent  of  the  other.  One  or  more  of  the  elements, 
which  analysis  showed  within  the  whole,  are  identified  with 
elements .  that  appear  outside  the  whole,  or  are  independent  of 
it.     We  have  here  Subtraction  or  the  Method  of  Difference. 

But  our  process  still  implies  a  centre  of  identity,  since  the 
grouping,  whether  it  conjoins  or  separates,  must  be  carried 
on  from  one  common  point  of  attraction  or  repulsion.  That 
point  however  will,  according  to  the  case,  be  manifest  or 
invisible. 

§  14.  And  coming  in  the  end  to  Disjunctive  Reasoning, 
under  which  head  falls  the  Apagogic  Method,  we  may  verify 
once  more  our  general  law.  Where  the  possibilities  are  given 
us  within  the  unity  of  the  given  subject  A,  it  is  solely  because 
they  are  identified  in  this,  that  b,  c,  and  d  are  found  to  be  dis- 
crepant. Their  relation  to  this  centre  thus  interrelates  them. 
And,  in  the  further  operation  of  removing  one  part  so  as 
to  predicate  the  residue,  our  construction  and  subsequent 
elimination  must  rest  on  the  basis  of  an  ideal  mid-point.  We 
have  discussed  this  already  by  anticipation,  and  it  is  not  worth 
while  to  repeat  the  argument. 

When  once  more  the  possibilities  of  A  are  not  given  us, 
and  when  we  make  them  ourselves  by  a  free  suggestion,  then 
so  far  the  process  is  constructive  synthesis.     We  should  not 


Chap.  V.]    ANOTHER  FEATURE  OF  INFERENCE.        429 

think  of  cor  d  in  connection  with  A,  if  there  were  no  reasoyi  for 
their  appearance.  And  the  reason  Hes  in  common  points  of 
sameness  7  and  S.  It  is  on  the  strength  of  these  that  c  and  d 
are  connected  with  A,  and  when  we  find  that  the  suggested 
connection  will  not  hold,  we  can  discover  that  it  was  a 
mistaken  inference  upon  the  ground  of  identity. 

§  15.  The  result  of  this  perhaps  too  brief  survey  may  be 
summed  up  thus.  Not  only  does  inference  preserve  an 
identity  throughout  the  whole  process,  but  in  the  actual 
experiment  itself  we  rest  upon  a  central  sameness.  There  is 
a  point  of  unity  in  every  operation,  and  each  special  operation 
has  a  special  point  of  unity.  We  have  thus  recovered  that 
earliest  view  with  respect  to  inference,  which  seemed  torn 
away  from  us.  But  it  does  not  return  intact.  We  can  not 
call  the  conclusion  in  all  respects  the  necessary  outcome,  and 
we  have  not  got  a  given  point  in  two  given  relations,  which 
thus  interrelates  them  to  form  our  conclusion.  That  con- 
clusion in  some  cases,  we  have  seen,  is  not  made  unless  we 
choose  to  make  it ;  and  the  arbitrary  character  inherent  in 
these  processes  gives  rise  to  doubt  and  to  grave  suspicion. 
In  the  Second  Part  of  this  present  Book  these  doubts  will  be 
considered  :  but  we  must  first  endeavour  more  exactly  to 
apprehend  the  operations  we  have  just  been  passing  in 
review. 


430  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt   L 


CHAPTER  VI. 

THE   FINAL  ESSENCE   OF   REASONING. 

§  I.  If,  considering  once  more  the  processes  we  have 
surveyed,  we  ask  for  the  principles  which  underlie  them,  we 
discover  first  of  all  the  Axiom  of  Identity.  What  is  true  in 
one  context  is  true  in  another,  and  what  holds  of  a  subject 
within  an  experiment  is  valid  also  beyond  that  experiment. 
And  when,  advancing  from  this,  we  approach  our  array  of 
ideal  ^  operations,  we  see  that  they  fall  under  analysis  and 
synthesis.  These,  if  we  take  in  that  other  principle  of  move- 
ment, by^which  we  go  from  the  possible  to  the  actual,  seem 
to  cover  the  ground  of  all  our  material.  On  the  Axiom  of 
Identity  we  propose  to  say  nothing  more  at  present,  but  there 
is  much  in  the  rest  which  remains  unexplained.  Let  us  for 
the  moment  dismiss  the  principle  of  transition  from  a  sur- 
viving possibility,  and  let  us  turn  our  attention  to  analysis  and 
synthesis.  Although  at  the  cost  of  a  partial  repetition  we 
must  try  to  penetrate  their  more  hidden  nature. 

§  2.  We  may  begin  by  asking  an  obvious  question,  Are 
these  two  operations  really  two,  and,  if  so,  in  what  sense  ? 
Are  they  unconnected,  that  is,  and  two  alien  species  of  a 
single  genus,  or  have  they  something  in  common  beyond  the 
universal  type  of  inference  ?  The  answer  to  this  question 
leads  straight  to  the  conclusion  which  we  are  to  reach.  We 
shall  try  to  show  that  analysis  and  synthesis  have  so  much  in 
common  that  they  are  actually  identical.  They  are  two 
different  sides  of  one  single  operation,  and  you  never  can 
hav^  one  without  having  the  other.  Hence  though  different 
they  are  the  same. 

§  3.  And  they  are  the  same  in  this  way.  Take  an  act  of 
analysis  in  which  A  becomes  (A)  dcd.  The  elements  in  the 
result  come  to  us  as  separate,  but  this  very  separation  involves 


Chap.  VI.]       THE   FINAL   ESSENCE   OF   REASONING.  43 1 

a  relation.  They  are  distinguished  by  virtue  of  a  central 
identity,  and  they  stand  thereby  in  some  kind  of  relation 
with  one  another.  But  this  relation  is  synthetical.  It 
did  not  exist  before  the  operation,  and  has  resulted  from 
it.  Thus  the  analysis,  whilst  analyzing,  has  shown  itself 
synthesis. 

Now  take  an  act  of  synthesis.  We  have  A  — B,  B  — C, 
and  from  this  we  go  on  to  produce  A  —  B  —  C.  We  have  got 
to  a  relation  which  before  was  absent ;  but  our  process  is  also 
an  act  of  analysis.  For  A,  B,  and  C  are  now  related  within 
a  whole  :  these  terms  and  their  relations  are  the  constituent 
elements  of  the  whole  A  —  B  —  C.  And  yet,  as  these 
members,  they  did  not  exist  and  could  not  exist  till  that 
whole  was  realized.  Thus  the  synthesis  has  analyzed  while 
it  seemed  but  to  conjoin. 

Summing  up  the  above  we  may  state  it  so.  Analysis  is 
the  synthesis  of  the  whole  which  it  divides,  and  synthesis  the 
analysis  of  the  whole  which  it  constructs.  The  two  processes 
are  one. 

§  4.  Bjit  with  all  their  unity  they  are  still  very  different, 
for  they  are  opposite  aspects  and  sides  of  one  movement,  and 
are  held  apart  by  three  special  diversities.  In  the  first  place 
(i)  the  given  material  is  different.  In  the  second  place  (ii) 
the  product  is  not  the  same.  And  finally  (iii)  the  operation 
of  which  we  are  conscious  differs  in  each  case.  Let  us  take 
these  in  order. 

(i)  In  analysis,  first,  we  do  not  go  beyond  the  area  which 
is  supplied  at  the  beginning.  The  whole  is  given,  and  we 
work  upon  that  whole  to  produce  a  synthesis  of  elements 
within  it.  We  do  not  travel  outside  our  explicit  starting- 
place,  and  hence  we  may  say  that  analysis  is  the  iiitenial 
synthesis  of  a  datum.  But  in  synthesis  we  find  that  the 
opposite  holds  good,  for  the  whole  is  not  given  any  longer, 
but  is  made.  Our  act  is  the  analysis,  not  of  our  visible 
starting-place,  but  of  something  implied,  unseen,  and^ideal. 
In  other  words  the  totality  emerges  for  us  in  the  product. 
Thus  in  analysis  we  operate  upon  an  explicit  whole,  and 
proceed  to  its  invisible  inside.  In  synthesis  we  begin  with  an 
organic  element,  or  elements,  not  seen  to  be  such  ;  and  passing 


432  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

beyond  each  to  what  is  outside,  so  bring  out  the  invisible 
totality  which  comprehends  them.  This  difference  of  start  is 
the  first  point  of  diversity. 

§  5.  And  it  leads  to  the  second  (ii).  As  the  material 
supplied  is  in  each  case  different,  so  again  the  product  is  not 
the  same.  In  one  case  the  whole  precedes  and  is  followed  by 
its  internal  relations  ;  but  in  the  other  case  external  relations 
come  first  and  so  produce  the  whole.  Where  the  result 
appears  as  the  further  determination  of  a  given  element  by 
something  outside  it,  the  process  is  synthetical.  Where  the 
result  gives  a  view  of  something  that  lay  hid  within  the  given, 
the  process  is  analytical.  Thus  it  is  analysis  where  your 
conclusion  falls  within  the  boundary  of  your  original  premise  ; 
but  it  is  synthesis  where  the  conclusion  falls  beyond  each 
premise  and  transcends  its  limits.  Analysis  is  the  inward 
synthesis  of  a  datum,  in  which  its  unseen  internal  elements 
become  explicit.  Synthesis  is  the  analysis  of  a  latent  whole 
beyond  the  datum,  in  which  the  datum  becomes  explicit  as 
a  constituent  element,  bound  by  interrelation  to  one  or  more 
elements  likewise  constituent.     This  is  the  second  diversity.  • 

§  6.  And  the  third  is  implied  (iii).  For  with  each  we  are 
conscious  of  a  different  side  in  our  one  operation.  In  analysis 
we  do  not  keep  sight  of  the  synthesis,  and  in  synthesis  we 
forget  the  act  of  analysis.  In  the  former  case  we  start  with 
an  unity,  we  break  this  up  by  a  function  of  diversity,  and 
ignore  in  the  result  both  the  unity  that  was  given  and  the 
function  that  was  applied.  The  product  presents  us  with 
separate  elements ;  but  these  elements  were  got  by  ideal 
discretion  operating  upon  an  original  continuity.  This 
given  continuity,  and  this  ideal  discretion,  are  not  visible  in 
our  conclusion ;  though  implied  they  are  latent.  But  in 
synthesis  the  unity,  latent  at  first,  becomes  explicit  in  the 
end,  and  what  we  ignore  is  its  previous  activity.  The  con- 
struction, that  was  wrought  on  the  original  discretion,  was 
the  ideal  function  of  the  final  unity.  But  this  we  forget,  and 
at  last  are  unaware  that  the  elements,  which  seem  to  have 
made  the  whole,  can  more  truly  be  said  to  have  been  found 
within  it.     Let  us  try  to  state  this  otherwise. 

We   may   say  that   in   analysis   the   given   becomes   the 


Chap.  VI.]       THE   FINAL   ESSENCE   OF   REASONING.  433 

continuity  of  fresh  discretes,  while  in  synthesis  it  becomes  one 
single  discrete  in  a  new  seen  continuity.  But  our  conscious- 
ness of  this  process  is  in  each  case  fragmentary.  For  in  one 
we  ignore  the  continuity  of  the  product,  and  in  the  other  we 
forget  its  once  helpless  discretion.  In  analysis  we  employ  a 
function  of  plurality  in  unity,  in  synthesis  we  use  a  function 
of  unity  in  plurality  ;  and  we  do  not  .f^^ .either.  In  the  result 
of  the  first  we  throw  away  the  continuity  on  which  we 
worked ;  and  emphasize  only  that  hidden  discretion  which 
before  was  latent.  In  the  result  of  the  last  we  reject  the 
original  hopeless  discretion,  and  emphasize  that  continuity 
which,  with  its  ideal  activity,  we  before  ignored.  In  both 
analysis  and  synthesis  what  is  used  is  not  seen.  An  unseen 
discretion  is  the  agent  which  procures  for  us  known  discretes, 
and  an  implicit  continuity  makes  behind  our  backs  an 
explicit  co7itimmm.  But,  if  so,  in  these  processes  we  have 
found  difference  with  identity,  identity  with  difference. 

§  7.  If  we  do  not  object  to  clumsy  forms,  we  may 
symbolize  our  general  doctrine  thus.     In  analysis  the  given 

X 

A,  plus  function  /\^  ,  gives  a  conclusion  b  —  c.     But  in  the 

^       1 
result  we  forget  that  ^  and  7  have  no  validity  except  within 
x;    and    that    hence    b  —  c   must   imply   the   whole  A.      In 
synthesis  again  we  start  with  A  —  B,  B  —  C  ;  and  this  datum, 

/3-7-S 
plus  a  function    \    /  ,  produces  A  -  B  -  C.      But  here  we 

X 

forget  that,  without  our  function,  A  —  B  and  B  -  C  stand  sun- 
dered by  a  gulf;  and  that  in  our  result,  where  they  appear 

A— B— C 
in  unity,  they  are  really  the  analysis  of  a  whole     \     I     / 

which  before  was  latent.  x 

It  is,  I  think,  scarcely  worth  while  to  enlarge  on  this 
head.  We  perhaps  have  said  enough  to  show  how  synthesis 
and  analysis  are  essentially  connected.  With  all  their 
diversity  they  are  but  different  sides  of  one  radical  principle. 

§  8.  If  this  is  true  when  we  apply  the  principle  un- 
consciously, it  continues  to  be  true  at  a  later  stage.  We 
may  deliberately  adopt  the  so-called   Analytic  or  Synthetic 

2  F 


434  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  L 

Method,  and  there  is  of  course  a  real  difference  between  them. 
But  the  result  is  always  a  two-sided  product.  In  the 
Synthetic  Method  we  begin  with  first  principles,  which  are 
stated  explicitly,  and  work  our  way  down  to  the  individual 
facts.  We  thus  constructively  build  up  a  whole  ;  but  all  the 
while  we  are  unconsciously  analyzing.  In  carrying  our 
principles  out  into  the  detail,  and  in  showing  the  detail  as  a 
consequence  of  those  principles,  we  are  really  breaking  up  the 
vague  general  idea  with  which  we  started,  and  our  whole 
developement  rnay  be  taken  as  setting  forth  the  particulars  of 
this  implicit  whole.  The  same  twofold  character  exhibits 
itself  when  we  apply  what  is  called  the  Analytic  Method. 
Starting  here  with  the  confused  appearance  of  the  whole,  we 
break  up  and  pierce  into  its  sensuous  concretion.  Thus  we 
make  our  way  to  the  relations  of  elements  more  and  more 
abstract,  what  in  short  are  termed  Laws.  But  these  Laws  are 
syntheses  ;  and  thus  the  analysis  which,  if  fully  carried  out, 
would  be  the  entire  destruction  of  the  first  confused  whole, 
reconstructs  that  whole  as  a  world  of  abstract  connections. 
It  is  everyday  experience  that  the  analysis  of  a  subject  shows 
its  internal  unity. 

This  reflection  may  prevent  our  staggering  at  the  truth  of 
a  weighty  paradox  ;  "  Knowledge  advances  from  the  abstract 
to  the  concrete."  The  confused  whole,  that  is,  which  comes 
before  our  senses  and  pours  out  its  riches,  goes  bankrupt 
when  we  refuse  to  accept  such  payment  and  insist  on  receiving 
universal  truth.  Or,  we  may  say,  the  felt  concrete,  when 
distilled  by  thought,  yields  at  first  but  a  thin  and  scanty 
result.  The  intellectual  product,  which  first  comes  over,  is  a 
connection  whose  actual  truth  holds  only  of  a  fraction  of  the 
subject.  It  is  not  till  we  have  gone  further  down  to 
principles,  that  our  intellectual  results  spread  over  the  whole 
field  and  serve  to  unite  the  mass  of  detail.  In  becoming  more 
abstract,  we  gradually  reach  a  wider  realm  of  ideas  ;  which 
is  thus  not  sensibly  but  intellectually  concrete.  What  is 
abstract  for  one  world  is  concrete  in  the  other. 

§  9.  At  this  point,  when  we  remember  some  too  hard 
sayings  on  the  comparative  worth  of  these  different  cur- 
rencies, we  feel  tempted  to  digress  and  humbly  to  protest. 


Chap.  VI.]       THE   FINAL  ESSENCE   OF   REASONING.  435 

But  we  must  hasten  onwards,  for  we  have  now  to  make 
another  remark  on  the  reciprocal  implication  of  these  two 
Methods.  Induction  is  of  course  considered  to  be  "  ana- 
lytical ;  "  but,  if  we  understand  induction  in  its  primitive  sense, 
and  use  it  for  that  collecting  of  instances  which  gives  an  uni- 
versal, the  synthesis  is  obvious.  For  we  not  only  get  internal 
connections  in  our  given  material,  but,  travelling  far  beyond  it, 
we  take  it  as  one  member  in  a  group  of  instances.  Beginning 
with  the  individual'  case  we  are  investigating,  we  go  on  to 
others  of  the  self-same  nature.  We  subsume  under  the  uni- 
versal which  we  have  implicit  in  our  original  datum.  Thus 
unawares  we  are  using  a  synthetic  construction  from  an 
identical  point ;  and,  by  the  actual  employment  of  this  latent 
universal,  we  make  it  in  the  end  explicit  and  visible. 

We  may  find  the  same  unconscious  substitution  of  process 
in  our  use  of  the  Synthetic  Method.  When  facts  are  ex- 
plained by  the  Synthetic  Method,  they  are  actually  ana- 
lyzed. We  reconstruct  the  phenomenon  which  we  have  under 
enquiry,  and  build  it  up  ideally  by  an  union  of  elements,  and 
thus  show  it  as  the  intersection-point  of  our  Laws.  And  this 
is  not  all.  Our  synthesis  never  quite  exhausts  the  fact ; 
there  is  left  an  unessential,  sensuous  element,  which  is  put  on 
one  side  as  irrelevant  matter.  And  this  residual  product,  left 
by  the  analysis  which  dissects  the  fact,  may  be  highly  impor- 
tant. In  comparing  it  with  our  ideal  reconstruction,  we  may  find 
a  vital  discrepancy,  before  unseen.  In  this  way  our  rebuilding, 
with  its  subsequent  contrast,  may  disclose  a  feature  in  the 
case  which  otherwise  would  have  escaped  perception.  Our 
synthesis  has  once  more,  and  in  this  additional  respect,  turned 
out  analytical. 

§  10.  It  is  not  in  principle  alone  that  analysis  and 
synthesis  are  essentially  one,  but  in  practice  also  their  unity 
tends  to  show  itself  in  the  product.  Performing  one  opera- 
tion we  find  that  we  have  also  accomplished  the  other ;  and 
we  may  err  in  our  estimate  of  the  relative  importance  and 
prominence  of  their  aspects.  As  an  instance  of  this  blindness, 
I  should  like  once  more  to  bring  on  the  stage  the  so-called 
Analytical  Psychology.  There  is  no  doubt  that  this  possesses 
a  right  to  its  name  ;  for  its  object  is  to  resolve  the  phenomena 

2  F  2 


436  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

of  the  soul  into  groupings  and  blendings  of  simple  elements. 
But  it  is  blind  not  to  see  that  its  procedure  is  just  as  much 
synthetical,  since,  starting  with  certain  elements  and  their  laws,  it 
attempts  to  reconstruct  and  build  up  ideally  the  complex  facts 
that  are  actually  experienced.  And  this  process  is  of  course 
the  Synthetical  Method. 

This  criticism  holds  even  if  we  admit  every  claim  put  forth 
by  our  English  school.  Even  if  the  original  elements  and  their 
laws  have  been  got  by  means  of  a  preliminary  analysis,  it  may 
yet  be  true  that  in  subsequent  practice  the  analytical  reduction 
of  particular  phenomena  is  effected  a  priori  by  a  constructive 
synthesis.  The  "  analysis  "  for  instance  of  visual  extension 
does  not  proceed  by  anatomy  of  what  is  given,  but  rather 
by  the  selection  of  factors  which  together  might  have  formed 
it.  Thus  when  the  claim  of  the  school  is  fully  admitted, 
we  must  still  point  to  blindness ;  and  it  is  possible  to  take  a 
more  unfavourable  view.  The  elements,  it  may  be  said, 
if  reached  by  analysis,  are  reached  by  an  analysis  which 
ignores  important  tracts  of  the  subject.  And  again  in  part 
they  are  not  reached  by  psychological  analysis  at  all.  On 
the  contrary  they  are  importations  of  coarse  physical  ideas, 
unacknowledged  borrowings  from  crude  metaphysics,  precon- 
ceptions introduced  without  any  warrant.  The  analysis  is  in 
short  accused  of  resting  on  a  vicious  construction  a  priori. 

§  II.  We  first  saw  that  all  inferences  could  be  reduced  to 
the  acts  of  synthesis  and  analysis,  plus  another  function.  We 
have  now  seen  that  analysis  and  synthesis  are  branches  from 
a  single  stem.  And  it  is  time  that  we  turned  to  search  for 
the  nature  of  this  other  element.  But  we  are  tempted  to 
make  first  a  fresh  enquiry  in  connection  with  the  processes 
which  we  have  just  discussed.  If  analysis  and  synthesis  are 
thus  entangled  at  the  root  of  reasoning,  what  bearing  has  this 
on  another  question  which  we  asked  before  (Chap.  IIL  §  ii). 
There  was  a  doubt  if  every  judgment  was  not  an  inference, 
and  the  doubt  seems  now  to  have  gathered  strength.  For  it 
may  be  asked.  Does  not  every  judgment  involve  a  synthesis 
and  analysis,  and,  if  so,  is  not  each  one  therefore  an  argu- 
ment ?  We  will  begin  with  the  first  question,  and  then  take 
the  second. 


Chap.  VI.]       THE   FINAL   ESSENCE   OF   REASONING.  43/ 

§  12.  Let  us  imagine  a  judgment  before  any  reproduction 
has  taken  place.  Certainly  no  such  judgment  could  exist, 
since  judgment  proper  appears  long  after  redintegration  has 
been  used,  and  is  a  consequence  of  that  use — but  for  argument's 
sake  let  us  suppose  such  a  judgment  which  comes  straight  from 
presentation. 

Even  such  a  supposed  judgment  would  still  exhibit  both 
analysis  and  synthesis.  It  would  in  the  first  place  analyze  for 
this  reason  :  the  whole  sensuous  datum,  the  totality  which 
appears,  never  can  be  ideally  mastered  by  thought  so  as  to  be 
intellectually  referred  to  reality.  For  apart  from  a  native 
tendency  of  the  mind  in  an  opposite  direction,  we  have  a 
sufficient  cause  in  impotence.  *  Do  what  we  will,  we  can  not 
take  up  every  single  detail  of  the  sensuous  mass.  We  must 
neglect  something;  but  the  dropping  of  part  is  the  forced 
selection  of  the  part  which  remains.  Hence  we  have  used  com- 
pulsory and  unwilling  abstraction,  and  that  means  analysis. 

But  this  judgment  is  on  the  other  side  synthetical 
The  content  which  it  has  selected  is  complex ;  it  involves 
elements  in  relation,  which  the  joint  selection  binds  together  in 
our  minds  ;  and  this  is  synthesis.  Nor  will  it  avail  to  object 
that  some  predicates  of  the  reality  seem  to  be  simple,  and  that 
here  at  all  events  we  have  no  synthesis  within  the  ideal 
content.  For  in  all  such  cases  an  element  of  content  would 
be  found  in  the  reality  which  stands  as  the  subject.  The  real 
subject  will  appear  in  union  with  a  certain  general  or  special 
appearance,  and  this  appearance  is  implicitly  a  part  of  that 
which  we  mean  to  say  of  the  ultimate  reality  (cf  p.  109). 
This  is  still  true  where  we  predicate  of  the  whole  given  fact  (p. 
56)  ;  for  we  connect  some  character  of  that  whole  with  our 
adjective,  and  take  both  as  qualities  of  the  real  subject ;  and 
thus  in  effect,  though  not  ostensibly,  both  fall  within  the 
predicate.  We  can  not  have  the  given  either  as  simple  being 
or  as  a  sensuous  felt  mass  without  character  or  feature  ;  *  and 

*  In  metaphysics  it  is  necessary  to  keep  this  in  view.  When,  for 
example,  we  argue  that  without  a  Permanent  no  change  could  be  ex- 
perienced, we  should  remember  that  on  the  other  side  it  may  be  urged 
that,  unless  this  Permanent  were  itself  phenomenal,  it  could  not  be 
effective,  and  that  the  fact  of  there  being  something  stable  in  phenomena 
seems  deducible  from  no  principle. 


438  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  L 

hence,  in  referring  to  the  real,  we  attend  to  and  we  mean  the 
real  as  qualified  in  a  certain  way.  This  quality  can  not  be 
said  to  become  an  idea,  yet  it  is  unconsciously  united  with  the 
ideal  content.  We  may  therefore  say  that,  if  we  go  back  far 
enough,  all  judgment  does  informally  predicate  a  connection 
which  is  'synthetical,  and  which  is  the  analysis  of  that  real  of 
which  it  is  predicated. 

§  13.  It  would  be  no  answer  to  reply  that  in  many  judg- 
ments we  seem  quite  passive.  For  in  all  these  judgments  we 
can  show  a  selection  and  again  a  conjunction,  and  we  may  argue 
that  hence  there  can  be  no  judgment  in  which  we  are  not 
active.  True,  I  admit,  that  we  do  not  actively  go  about  to 
join  and  select.  True  again  in  some  cases  that  we  never 
selected,  nor  should  have  dreamt  of  joining,  and  that  the  act 
is  little  but  the  formal  acceptance  of  a  conjunction  forced  upon 
us  from  without.  I  fully  admit  this,  but  it  seems  in  no  way  to 
shake  my  assertion. 

Assume,  as  we  must,  that  our  intellect  is  not  answerable 
wholly  for  the  matter  which  it  perceives  in  our  sensible  judg- 
ments. Assume  that  it  has  no  intelligible  ground  for  many  of 
the  events  which  it  is  forced  to  register.  Recognize  the  fact 
that  mere  chance  strength  of  stimulus,  blind  emphasis  of  sense, 
is  the  reason  why  our  perception  was  thus  and  was  not  other- 
wise. Acknowledge,  in  the  end,  that  whatever  intellectual 
assimilation  by  affinity  you  may  fairly  suppose  to  have 
worked  unconsciously — yet  at  last  the  effective  condition  of  the 
judgment  is  found  in  mere  sensuous  depression  and  relief ; 
that  it  was  by  this  that  a  part  of  the  presentation  was  sunk, 
and  the  rest  left  standing  in  a  prominent  conjunction.  But,  I 
repeat,  all  this  is  nothing  to  the  purpose  ;  we  here  have  got 
the  sine  qua  non^  but  we  have  got  nothing  else. 

The  intellect  in  judgment  may  be  guided  and  led  by 
irrational  suggestions,  and  yet  that  judgment  after  all  may  be 
an  intellectual  act.  For  the  sensuous  emphasis  which  prompts 
and  directs  disappears  in  the  result,  and,  however  the  mind 
has  come  to  its  judgment,  after  all  it  has  judged.  The 
selection  and  relation,  which  appears  in  the  product,  is  not  the 
mere  blurring  and  accentuation  of  sense.  It  may  have  been 
influenced  by  it,  and  arisen  from  it,  but   its   essence   is  now 


Chap.  VI.]        THE   FINAL   ESSENCE   OF   REASONING.  439 

diverse.  Bare  difference  is  one  thing  and  distinction  is  another  ; 
solicitation  and  tempting  prominence  are  still  not  recognition  ; 
and  we  may  be  forced  to  notice,  but  after  all  we  notice. 
Judgment  is  our  act ;  and  the  separation  and  integration,  which 
appear  in  its  content,  are  the  work  of  our  own  analysis  and 
synthesis,  compelled,  if  you  will,  but  none  the  less  active. 

§  14.  From  mere  strength  and  weakness  of  feeling  on  one 
side,  you  can  not  cross  to  the  other  side  by  degrees,  and  reach 
without  a  break  a  relation  of  content  referred  to  reality.  The 
distinction  and  separation,  which  appear  first  in  judgment, 
imply,  as  we  have  seen,  both  analysis  and  synthesis.  The 
perceived  exclusion  of  one  element  by  another  involves  their 
relation,  and  hence  their  unity  in  an  embracing  whole.  And 
the  existence  of  this  central  unity  is  obvious  in  every  con- 
junction. Let  that  be  ever  so  external,  it  still  presupposes  a 
point  of  identity  ;  and  it  is  synthesis  within  a  whole  which  is 
so  differentiated  and  therefore  analyzed. 

We  may  thus  state  our  result.  All  judgment  necessarily 
contains  a  relation ;  but  every  relation,  beside  its  pair  of 
related  elements,  presupposes  an  unity  in  which  they  subsist. 
Hence  the  judgment,  in  so  far  as  it  is  the  synthesis  of  the 
elements,  is  just  so  far  the  analysis  of  that  whole  to  which 
they  belong.  And,  since  the  experience  into  which  our  sen- 
suous suggestions  have  to  be  translated,  bears  this  character 
— a  character  not  in  the  same  way  possessed  by  those  sugges- 
tions themselves — we  may  say  that  all  judgment,  however 
near  to  sense,  is  essentially  an  act  of  analysis  and  synthesis. 

§  15.  Our  first  question  has  thus  been  answered  affirma- 
tively. Let  us  now  come  to  the  second.  If  judgment  is  an 
act  of  analysis  and  synthesis,  is  it  true  that  therefore  judgment 
is  an  inference  ? 

The  answer  which  before  (Chap.  III.  §§  12-18)  we  gave 
in  the  negative,  seems  now  threatened  with  reversal.  Inference 
so  far  has  been  found  reducible  to  a  double  process  of  synthesis 
and  analysis  ;  and  it  seems  that  such  a  process  exists  also  in 
judgment.  Must  we  not  then  say  that,  as  reasoning  implies 
judgment,  so  judgment  implies  reasoning  .?  We  can  not  say 
this,  and  a  distinction  remains  which  it  is  impossible  to  break 
down.     Inference  is  an  experiment  performed  on  a   datum, 


440  THE   PRINCIPLES   OF  LOGIC.  [Bk.  III.  Pt.  I. 

which  datum  appropriates  the  result  of  the  experiment.  But 
in  those  judgments  of  perception,  which  we  have  been  just 
discussing,  there  is  properly  no  datum.  I  do  not  mean  that, 
like  the  Deity  of  our  childhood,  they  create  their  world  from 
nothing  at  all,  and  exert  their  activity  on  a  void  externality  or 
their  own  inner  emptiness.  What  I  mean  is,  that  the  basis, 
from  which  they  start,  and  on  which  they  act,  is  for  the  intellect 
nothing.  It  is  a  sensuous  whole  which  is  merely  felt  and 
which  is  not  idealized.  It  is  not  anything  which,  as  it  is, 
could  come  before  an  understanding ;  and  hence  we  can  not 
take  it  as  the  starting-point  of  inference,  unless  we  are  ready 
to  use  that  term  in  a  somewhat  loose  sense. 

We  needs  must  begin  our  voyage  of  reasoning  by  working 
on  something  which  is  felt  and  not  thought.  The  alteration  of 
this  original  material,  which  makes  it  first  an  object  for  the 
intellect,  is  thus  not  yet  inference,  because  the  start  has  not 
been  made  from  an  ideal  content.  Before  reasoning  exists, 
there  must  come  an  operation  which  serves  to  transform  this 
crude  material ;  and  this  operation  is  both  analytical  and 
synthetical.  But  it  is  not  inference ;  for,  though  its  result  is 
intellectual,  its  premise,  so  to  speak,  is  merely  sensuous. 

Thus  our  primitive  judgment  falls  short  of  inference  in  two 
main  points.  It  is  doubtful  first  (i)  if  the  operation  performed 
is  not  purely  capricious.  Psychologically,  of  course,  it  does 
not  come  by  accident ;  but  regarded  logically  it  looks  like 
chance.  We  have  no  rational  ground  we  can  produce,  in  order 
to  justify  our  result.  This  is  the  first  point ;  and  secondly  (ii) 
the  stuff,  upon  which  the  act  is  directed,  is  not  intellectual. 

§  1 6.  Thus  judgment  is  not  inference.  But  though  the 
answer  we  have  given  is  so  far  satisfactory,  it  ignores  a 
question  which  must  now  be  raised.  /'Both  judgment  and 
inference  are  terms  that  can  be  used  in  more  senses  than  one. 
They  may  stand  for  these  acts  at  the  highest  stage  of  their 
most  conscious  developement,  or  may  point  to  the  undeveloped 
and  early  rudiment  of  their  unconscious  beginning.  .  And  the 
question  is  whether  this  doubtful  meaning  has  not  seduced  us 
into  a  common  fallacy. 

The  evolution  of  the  mind  and  of  its  various  powers 
through  different  stages,  and  the  survival  and  co-existence  of 


Chap.  VI.]        THE   FINAL   ESSENCE   OF   REASONING.  44 1 

nearly  all  these  stages,  lead  us  everywhere  into  difficulty,  and 
threaten  us  with  illusion.  And  the  danger  lies  in  the  risk  of 
turning  through  a  vicious  circle.  For  two  so-called  faculties 
stand  to  each  other  in  such  a  way  that  each  one,  if  you  take  it 
at  a  higher  stage,  presupposes  the  other  in  a  less  advanced 
form  of  developement.  Each  therefore  in  some  sense  does 
start  from  the  other  ;  and,  if  you  forget  that  sense,  you  are 
tempted  to  make  the  dependence  absolute.  While  both  are 
co-equal,  you  may  falsely  place  one  in  front  of  the  other.  This 
is  as  common  a  mistake  as  can  be  found  in  psychology,  and 
we  may  seem  to  have  given  it  a  fresh  jUustration. 

For  we  argued  that  judgment  could  not  be  inference,  since 
inference  starts  from  an  intellectual  base,  while  early  judgment 
must  begin  with  sense.  And  the  doubt  is  whether  a  similar 
proof  would  not  show  that  inference  must  precede  judgment. 
Suppose  both  coeval,  and  progressing  through  stages,  then 
rudimentary  inference  will  come  before  explicit  judgment,  just 
as  primitive  judgment  was  required  as  a  base  for  explicit 
inference.  And  in  this  case  we  surely  should  have  fallen  into 
error,  for  reasoning  of  some  kind  would  be  implied  in  the  very 
beginnings  of  judgment. 

§  17.  We  did  not  make  this  mistake.  When  we  said  that 
some  judgment  was  free  from  inference,  we  knew  the  sense  in 
which  our  terms  were  used.  What  we  spoke  of  was  explicit 
judgment  and  inference,  acts  both  of  which  end  in  an  asserted 
truth,  and  one  of  which  starts  with  a  truth  laid  down  as  the 
foundation  of  its  process.  And  in  this  sense  it.  is  true  that  we 
judge  before  we  reason,  since  we  become  possessed  of  an 
affirmation,  when  we  can  not  produce  any  other  affirmation  upon 
which  this  stands.  Thus  the  distinction  which  we  made 
remains  unshaken.  Explicit  judgment  comes  before  explicit 
inference.  And  supposing  that  both  are  really  and  in  the  end 
two  sides  of  one  act,  then  the  above  conclusion  is  what  we 
might  have  expected.  Here  as  everywhere  the  product  comes 
to  consciousness  first,  and  the  process  afterwards. 

§  18.  Explicit  judgment  is  assuredly  distinct  from  explicit 
inference  ;  but  if  we  like  to  go  back  to  the  origin  of  each,  and 
ask  if  the  rudiment  and  beginning  of  one  comes  before  or 
after  the  rudiment  of  the  other — then,  I  think,  we  must  give  a 


442  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

different  answer.  The  earliest  judgment  will  imply  an  opera- 
tion, which,  though  it  is  not  inference,  is  something  like  it ;  and 
the  earliest  reasoning  will  begin  with  a  datum,  which  though 
kin  to  judgment,  is  not  intellectual.  And  from  the  first  these 
two  functions  imply  one  another.  You  can  not  say  that  in 
developement  either  comes  first ;  they  emerge  together  as 
two  sides  and  elements,  implicit  within  one  primitive  whole. 

If  we  begin  our  enquiry  from  the  physiological  side,  we  find 
there  a  process  which  consists  of  two  parts,  an  action  and  a 
reaction.  We  may  agree  to  say  that  experience  starts  with  a 
stimulation  coming  in  from  the  periphery  ;  but  then  this  is  but 
one  side,  for  the  stimulation  must  be  met  by  a  central  response. 
I  do  not  mean  that  experience  first  begins  with  a  motor 
discharge  ensuing  upon  an  incoming  shock.  That  may  be 
true,  but  something  else  and  more  general  is  to  be  considered 
here.  Unless  the  nerve-centre  answered  to  the  afferent 
impulse  by  some  kind  of  reaction,  whatever  it  may  be,  could 
we  say  that  there  existed  a  physiological  sensation  ?  It  seems 
clear  we  should  be  wrong  if  we  ventured  on  this. 

And,  if  we  consider  the  same  thing  from  its  psychical  aspect, 
we  shall  reach  the  same  result.  No  doubt  our  inherited 
superstitions  have  used  us  to  the  idea  of  sensations,  which 
simply  walk  into  a  mind  which  is  nothing  but  empty  space. 
But  is  this  idea  true  }  Is  it  not  being  slowly  but  surely 
exploded  by  the  doctrine  which  sees  in  every  sensation  the 
product  of  an  active  mental  reaction  }  We  may  say  then  that 
our  senses  give  us  sensations  ;  but  their  gift  contains  traces 
of  something  like  thought. 

§  19.  I  am  aware  of  the  difificulties  which  beset  this  subject, 
and  it  is  impossible  here  to  enter  into  them.  I  may  perhaps 
briefly  state  the  question  thus.  At  a  certain  stage  we  should 
all  admit  that  our  presentations  show  marks  of  intellectual 
activity.  Well,  as  you  follow  backward  these  presentations  to 
the  earliest  rudiment  which  you  can  say  is  given,  at  what 
point  will  you  draw  your  dividing  line  }  Where  will  you  say. 
We  have  here  the  crude  material,  which  would  be  exactly 
what  it  is  now,  though  there  were  nothing  like  comparison, 
reproduction,  or  abstraction  ?  And  non-success  in  finding  the 
proper  place  for  this  line,  may  lead  to  the  belief  that  no  place 


Chap.  VL]        THE   FINAL   ESSENCE   OF   REASONING^^^^  i.|2Sl^ -*'^^, 

is  proper,  and  that  no  known  material  is  wholly  crude, 
experience  is  not  intellectual,  in  the  sense  that  we  get  elements 
conjoined  and  parted  by  relations  which  explicitly  appear.  It 
does  not  give  us  an  ideal  content  marked  off  from  the  mass  of 
confused  reality,  and  internally  defined  as  qualities  in  relation. 
On  the  contrary  it  comes  as  a  vague  totality  which  has 
nothing  outside  it,  and  which  internally  is  felt  as  an  indis- 
criminate effect,  in  which  the  constituents  are  lost  to  view. 
But  it  is  intellectual  in  the  sense  that,  when  we  come  to  reflect 
on  its  dattnn^  we  find  marks  of  activities,  which,  if  they  had 
been  coiiscions,  and  if  they  had  not  stopped  at  feeling,  we  must 
have  called  intellect.  And  I  regret  to  say  that  I  must  leave 
the  matter  so. 

§  20.  But,  assuming  that  the  first  thing,  which  we  feel  or 
know,  results  from  a  reaction  upon  a  stimulus,  we  must  deny 
two  things.  We  must  refuse  to  allow  that  experience  comes 
from  an  operation  on  a  datum,  or  yet  is  a  datum  without  an 
operation  and  so  independent.  Both  assertions  would  suppose 
that  something  is  given,  where  nothing  is  yet  given.  The 
beginning  of  experience  is  the  resultant  of  two  factors,  a 
stimulus  and  a  response.  And  here  we  see  how  the  rudiments 
of  judgment  and  reasoning  are  intertangled.  The  mere  sti- 
mulus is  not  given,  and  so  reasoning  has  nothing  from  which 
it  could  start.  But,  on  the  other  hand,  a  mental  activity  can 
not  be  directed  upon  simple  zero.  We  have  two  factors,  the 
reaction  and  the  stimulus,  and  in  a  certain  and  improper  sense 
these  two  factors  may  be  taken  as  the  premises  of  a  judg- 
ment. And  the  result  again  may  be  taken  as  a  conclusion, 
not  indeed  from  data,  but  from  an  indefinite  ground  to  a 
definite  datum. 

§  21.  Nor  can  we  fairly  object  that  this  conclusion  is 
capricious,  that  the  activity  is  either  an  arbitrary  handling 
which  makes  its  result,  or  a  formal  registration  which  merely 
accepts  it.  Irrational  indeed  the  conclusion  must  be,  in  the 
sense  that  the  mind  can  give  no  reason  for  the  sensation  it  is 
forced  to.  But  capricious  or  formal  it  certainly  is  not.  It 
follows  from  its  premises  with  the  strictest  necessity,  and 
combines  in  its  result  the  character  of  both.  And  again  it  is 
no  mere  formal  acceptance.     For  the  organism,  and  with  it 


444  THE   PRINCIPLES   OF  LOGIC.  [Bk.  III.  Pt.  I. 

the  empirical  subject,  has  its  peculiar  nature  which  is  im- 
pressed on  the  product.  We  might  say  that  our  premises  are 
the  centre  and  the  incoming  change,  that  the  middle  operation 
is  the  synthesis  of  both,  and  that  our  result  is  the  conclusion. 
And  in  such  a  loose  and  incorrect  sense  of  the  term  this 
operation  is  inference. 

Or  let  us  take  the  same  thing  at  a  higher  remove.  Let  us 
pass  beyond  those  factors  which  first  produce  feeling,  and  let 
us  say  that  the  feeling  has  been  produced  and  qualifies  the 
subject.  But  one  feeling  is,  as  we  are  told,  no  feeling  ;  and 
the  subject,  merely  determined  as  a,  is  so  far  nothing.  Then 
while  a  remains,  let  /3  supervene,  and  the  result  may  now  be 
a  sensation  A,  which  is  neither  ^  nor  a,  but  is  the  consequence 
of  their  union.  This  result  is  clearly  no  inference  proper,  yet 
it  possesses  much  in  common  with  reasoning.  We  may  be 
said  to  have  premises  a  and  y8,  then  comes  their  synthesis, 
and  a  sensation  A  is  the  new  result.  Nor  is  it  easy  to  object 
that  at  all  events  for  consciousness  a  result  must  come  first, 
and  then  afterwards  be  used.  For  if  one  feeling  is  no  feeling, 
perhaps  consciousness  first  wakens  with  a  complex  presenta- 
tion, and  gets  by  a  circular  process  the  result  together  with  its 
premise.  The  first  feeling,  which  is  the  reason  why  we  ex- 
perience the  second,  itself  becomes  explicit  in  the  product,  and 
is  thus  both  starting-point  and  goal. 

§  22.  It  is  clearly  unsafe,  when  we  go  back  beyond  ex- 
plicit judgment,  to  give  priority  to  either  function.  It  is  better 
to  treat  their  rudimentary  forms  as  two  parts  of  one  whole ; 
and  it  is  this  point  of  view  from  which  it  would  be  right  to 
consider  the  nature  of  our  early  experience.  We  should  in 
this  case  be  led  to  ask  some  interesting  and  important 
questions.  If  in  knowledge  the  subject  and  the  object  are 
premises,  is  not  every  assertion,  which  confines  itself  to  the 
object,  an  illogical  conclusion  .?  No  physiologist  would  believe 
that  colours  or  sounds  were  the  properties  of  those  stimuli 
which  act  on  the  centres  of  vision  or  hearing.  But,  if  so,  by 
what  process  are  we  to  remove  the  influence  of  the  subject  in 
knowledge  } 

And  there  is  another  question,  the  importance  of  which 
could  not  well  be  exaggerated.     If  in  knowledge  the  subject 


Chap.  VI.]        THE   FINAL   ESSfiNCE   OF  REASONING.  445 

and  the  object  may  be  called  premises,  then  what  are  we 
to  say  of  the  middle  operation?  We  have  seen  that  this 
demands  a  central  identity,  and  where  is  the  central  identity 
here  ?  But,  without  it,  what  becomes  of  the  relation  of  the 
premises  and  of  the  ensuing  result  ?  This  question  would  lead 
to  problems  in  metaphysics  which  we  can  not  even  glance  at 
in  passing. 

§  23.  If  we  tried  to  pursue  this  line  of  enquiry,  we  should 
soon  be  carried  beyond  the  scope  of  our  volume.  But,  if  we 
return  to  the  immediate  object  of  our  scrutiny,  the  relation 
existing  between  judgment  and  inference,  we  may  show  how 
the  circle,  which  we  lately  noticed,  comes  up  in  the  process  of 
reproduction.  Every  judgment  on  the  one  hand  seems  to 
imply  redintegration,  which  itself  on  the  other  hand  seems  to 
presuppose  judgment.  The  explanation  is  that  reproduction 
implies  a  rudiment  of  judgment,  but  that  this  does  not 
become  explicit  and  show  itself  <3'j  judgment,  until  it  has  been 
used  as  a  basis  of  inference.  The  unconscious  synthetical 
activity  brings  its  own  principle  or  premise  before  our  eyes, 
and  in  a  sense  makes  that  actual.  And  we  have  here  no  miracle. 
We  are  given  ebf,  which,  by  redintegration  from  abed,  turns 
to  ebfd;  and  from  ebdf  an  abstraction  may  supply  us  with 
the  judgment  b  —  d.  But  this  b  —  d,  which  .is  thus  the  con- 
clusion, was  also  the  basis  of  our  reproduction. 

It  will  be  obj_ected  no  doubt  that  in  abed  there  perhaps 
may  be  no  rudiment  of  judgment ;  that  there  may  exist  in 
this  foundation  no  intellectual  act,  no  unconscious  selection,  or 
notice,  or  preferential  attention  to  b-d;  and  that  in  short 
there  may  be  nothing  but  sensuous  strength  and  prominence 
of  b  and  d.  But  in  the  end,  as  we  have  seen,  this  will  make 
no  difference.  For  it  is  admitted  that,  out  of  the  past  abed, 
b  —  d  IS  employed  to  qualify  ebf.  But,  if  so,  we  ask,  In  what 
shape  is  this  ^  —  ^  made  use  of.?  Can  it,  if  you  take  it  as  it 
comes  to  sense,  be  so  employed  at  all  }  This  would  be  quite 
impossible.  Beside  its  entanglement  with  the  whole  abed,  it 
has  in  itself  a  particular  character,  a  special  colouring,  which 
does  not  suit  ebf,  and  which  does  not  appear  in  the  con- 
clusion ebfd.  And  thus  the  purification  of  b  —  d  is  an 
intellectual   act,  performed  as  part  of  the  reproduction.     It 


446  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  L 

shows  clearly  that  function  of  selective  analysis  which  belongs 
to  judgment  and  to  inference  alike. 

§  24.  It  is  interesting  to  see  how,  when  we  qualify  a  per- 
ception through  reproduction,  our  act  is  one  common  process 
of  analysis  and  synthesis.  Let  abed  be  given,  and  then  ebf^ 
and  let  b  redintegrate  its  complement  d,  with  a  final  result 
b  —  d.  The  movement  is  synthetical,  and  yet  it  has  analyzed, 
since  it  has  divided  two  wholes.  In  the  first  place,  since  b  —  d 
has  never  been  given  us,  its  use  and  explicit  realization  breaks 
up  abcd^  and  is  thus  abstraction.  In  the  second  place,  now 
that  we  are  aware  oi  b  —  d  and  have  ebf  presented,  the  dif- 
ferent contexts  of  b  are  a  means  for  splitting  up  ebf.  The 
analysis  of  both  these  compounds  emerges  in  the  act  of  con- 
struction. 

I  will  work  out  more  in  detail  one  part  of  the  process  we 
have  just  observed.  Let  abc  be  presented,  and  then  let  b  be 
fixed  upon  and  considered  by  itself.  This  of  course  is  analysis, 
and  what  I  want  to  show  is  that  construction  can  effect  it. 
For  suppose  that,  on  the  strength  of  former  experience,  b  is 
now  an  element  in  other  connections.  Then  here  in  abc  the 
b  may  redintegrate  other  elements,  and  may  try  to  appear  as 
I,  ^p  oY  b  —  q  or  b  —  r,  all  disparate  with  one  another  and  with 
abc.  A  collision  must  follow  between  /,  q,  r  and  ac,  with 
the  result  that/,  q  and  r  are  rejected.*  But  this  rejection  may 
have  led  to  a  distinction.  The  identity  of  b  amid  these 
struggling  differences  may  have  caused  the  attention  to  be 
centred  upon  it.  In  the  process,  so  to  speak,  it  may  thus  have 
become  free,  and  hence  the  synthesis  will  have  been  a  con- 
dition of  analysis. 

We  are  invited  to  pursue  this  subject  further,  but  we  have 
done  enough  if  we  have  shown  the  interconnection  of  both  our 
functions.  We  must  return  from  our  digression  (if  it  really  be 
such),  and  must  take  up  the  thread  we  broke  off  before  in 

§11. 

§  25.  Beside  the  functions  of  analysis  and  synthesis  we 
found  that  reasoning  employed  a  third  principle.  The  leap 
of  transition  from  the  possible  to  the  real  did  not  seem  to  fall 
under  either  of  these  heads.      We  must  try  to  see  this  third 


Chap.  VI.]        THE   FINAL   ESSENCE   OF   REASONING.  447 

principle  more  clearly  ;  and,  if  the  reader  will  permit,  will 
approach  it  indirectly.  We  will,  try  to  show  how  the  defects 
of  analysis  and  synthesis  lead  the  mind  beyond  the  limit  of 
these  functions. 

We  have  seen  that  they  both  are  two  sides  of  one  process. 
And  it  follows  from  this  that  the  increase  of  one  must  add  to 
the  other.  The  more  deeply  you  analyze  a  given  whole,  the 
wider  and  larger  you  make  its  unity ;  and  the  more  elements 
you  join  in  a  synthetic  con.struction,  so  much  greater  is  the 
detail  and  more  full  the  differentiation  of  that  totality.  We 
have  here  the  antipodes  of  that  false  relation  of  extension  to 
intent  which  we  criticized  before  (Book  I.  Chap.  VI.).  That 
preposterous  article  of  orthodox  logic  turned  the  course  of  our 
reason  into  senseless  miracle.  The  less  a  thing  became  the 
further  it  went,  and  the  more  it  contained  the  narrower  it 
became.  Such  a  total  reversement  of  our  rational  instinct 
could  spring  from  nothing  but  a  fundamental  error.  And  it 
arose  from  our  use  of  the  abstract  universal.  That  can  not  be 
real,  and  in  consequence  our  thoughts  were  all  built  on  un- 
reality and  ended  in  falsehood.  But  in  the  concrete  universal, 
which  has  guided  our  steps,  and  which  has  appeared  as  the 
identity  of  analysis  and  synthesis,  we  have  returned  to  truth 
and  made  our  peace  with  reality. 

§  26.  If  for  metaphysics  what  is  individual  is  real  and  what 
is  real  individual,  for  logic  too  the  rational  is  individual  and 
individuality  is  truth.  And  this  is  no  paradox.  Our  practical 
criterion  in  every  enquiry  is  the  gaining  all  the  facts  and  the 
getting  them  consistent.  But  this  simple  test  unconsciously 
affirms  that  the  individual  is  true  and  the  truth  individual. 
For  a  fragment  of  the  whole  broken  off  abruptly,  or  a  whole 
that  internally  was  at  issue  with  itself,  would  alike  fall  short  of 
individuality.  Unawares  then  we  strive  to  realize  a  com- 
pletion, single  and  self-contained,  where  difference  and  identity 
are  two  aspects  of  one  process  in  a  self-same  substance,  and 
where  construction  is  self-diremption  and  analysis  self-syn- 
thesis. This  idea  of  system  is  the  goal  of  our  thoughts,  and 
to  sight  of  this  perfection  we  have  been  conducted. 

§  27.  But  we  have  not  reached  nor  entered.  Our  analysis 
and  synthesis  have  fatal  defects,  and  their  unity  is  poor  and 


448  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

but  superficial.  Our  analysis  has  to  begin  with  a  datum,  and 
to  divide  its  singleness  into  single  components.  But  in  the 
first  place  this  origin  is  not  single.  For  the  datum,  with 
which  it  begins,  is  limited,  and  is  therefore  defined  by  external 
relations.  These  alien  connections  go  to  make  it  what  it  is, 
and  it  hence  involves  them  within  its  own  being.  But,  if  so, 
its  unity  comes  to  an  end.  In  its  attempt  at  self-developement 
it  depends  on  the  external ;  and  therefore,  even  if  its  analysis 
is  successful,  it  has  not  analyzed  itself.  And  in  the  second 
place  the  result  of  its  analysis  remains  defective.  It  fails  not 
only  to  analyze  itself,  but  it  also  fails  to  carry  out  the 
analysis.  For  the  components  it  produces  are  themselves 
unstable.  Characterized  as  they  are  by  their  external 
relations  and  so  impregnated  with  a  foreign  principle,  their 
own  unity  falls  apart  internally  into  relations  of  other  in- 
cluded units  ;  and  hence  we  never  reach  anything  which  we 
could  rightly  call  single.  Want  of  individuality  in  the  datum 
that  we  began  with,  absence  of.  self-movement  and  impossi- 
bility of  self-developement,  this  is  the  first  defect.  Want  of 
individuality  in  the  result  attained,  and  endless  dissipation 
into  foreign  relations,  this  is  the  second  defect  of  our  analysis. 
It  is  ruined  throughout  by  externality.  The  elements  are 
inwardly  alien  to  themselves,  and  from  without  they  each  are 
alien  to  the  other  and  to  their  common  origin.  The  analysis. 
in  the  end  is  hence  not  synthesis,  if  that  means  self-relation. 

§  28.  And  our  synthesis  is  no  less  defective.  We  start 
with  one  element  and  go  on  to  another,  and  find  them  both  as 
constituents  in  a  whole.  But  we  can  not  say  that  we  advance 
from  our  datum  by  the  analysis  of  that.  The  opposite  is  the 
case,  for  our  fresh  constituent  is  dragged  up  and  chained  on 
from  the  outside.  To  the  original  element  this  stranger  does 
not  seem  a  part  of  itself,  but  a  foreign  arrival  and  importation. 
The  synthesis  is  thus  not  self-determination.  And  this  same 
fault  has  another  side.  For  the  whole,  which  you  have 
reached,  is  no  system  of  difTerences  ;  it  is  not  an  individual. 
The  difTerences  are  an  aggregate,  found  conjoined  together,- 
and  no  self-analysis  of  a  single  unity.  The  elements  certainly 
are  united  by  a  central  point,  and  are  thus  inter-related  ; 
but    their    relations    remain    external   and    forced.      Instead 


Chap.  VL]        THE   FINAL   ESSENCE   OF   REASONING.  449 

of  moving  freely  from  one  to  the  rest,  you  are  compelled  to 
pass  through  a  machinery  of  steps,  which  seem  to  have  no 
vital  connection  with  the  elements  you  bring  together. 
Thus  the  union  is  in  the  end  no  inward  bond,  but  a  foreign 
coupling ;  and  you  can  not  pass  from  the  centre  to  the 
system  of  differences.  It  is  no  living  point  that  withdraws 
into  itself  the  life  of  its  members,  and  flows  forth  into  a  body 
which  it  feels  as  its  own.  It  is  the  axle  of  a  wheel  where 
spokes  are  driven  in,  and  where  the  number  of  holes  and 
spokes  is  indifferent. 

This  first  fault  of  our  synthesis  implies  a  second  and 
counterpart.  For  the  whole,  which  we  make,  is  never  com- 
pleted. It  is  determined  from  outside  ;  and  its  unity  is 
compelled  to  assimilate  in  relations  to  foreign  bodies  the  seed 
of  dissolution.  These  bodies  fall  outside  that  whole  whose 
analysis  we  from  time  to  time  have  procured  by  our  synthesis. 
The  synthesis  turns  out  therefore  not  to  be  the  analysis  of 
the  whole  which  we  assigned  to  it,  since  that  whole  does  not 
include  the  foreign  matter,  which  intrudes  in  the  result.  And 
the  perpetual  effort  to  go  on  and  to  find  the  completion  of 
our  synthesis,  and  to  realize  the  unity  which  we  demand  in 
our  construction,  proves  a  self-delusion.  It  leads  to  that 
chase  of  the  spurious  infinite,  where  fruition,  ever  instant,  is 
baulked  perpetually.  Our  synthesis  is  therefore  no  self- 
analysis.  / 

§  29.  We  have  seen  the  defects  in  both  sides  of  our 
operation,  and  we  naturally  ask.  Is  there  any  remedy }  Or, 
since  the  sin  lies  so  deep  that  to  remedy  the  process  would  be 
to  change  its  nature,  we  may  ask.  What  is  it  that  we  really 
do  want }  What  was  it  that  guided  our  half-conscious 
thoughts,  and  forced  us  to  see  failure  where  we  desired 
success  1  To  perceive  imperfection  is  to  judge  by  the  perfect, 
and  we  wish  to  become  aware  of  this  idea  which  has  served  us 
as  a  canon  and  touchstone  of  reason.  If  we  realized  our  ideal, 
what  then  should  we  get } 

We  should  get  a  way  of  thinking  in  which  the  whole  of 
reality  was  a  system  of  its  differences  immanent  in  each 
difference.  In  this  whole  the  analysis  of  any  one  element 
would,  by  nothing  but  the  self-developement  of  that  element, 

2  G 


450  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Ft.  I. 

produce  the  totality.  The  internal  unfolding  of  any  one 
portion  would  be  the  blossoming  of  that  other  side  of  its 
being,  without  which  itself  is  not  consummate.  The  inward 
growth  of  the  member  would  be  its  natural  synthesis  with  the 
complement  of  its  essence.  And  synthesis  again  would  be 
the  movement  of  the  whole  within  its  own  body.  It  would 
not  force  its  parts  into  violent  conjunctions,  but,  itself  in  each, 
by  the  loss  of  self-constraint  would  embrace  its  own  fulfilment. 
And  the  fresh  product  so  gained  would  renew  this  process, 
where  self-fission  turns  to  coition  with  an  opposite  and  the 
merging  of  both  in  a  higher  organism.  Nor  would  the  process 
cease  till,  the  whole  being  embraced,  it  had  nought  left 
against  it  but  its  conscious  system.  Then,  the  elements 
knowing  themselves  in  the  whole  and  so  self-conscious  in  one 
another,  and  the  whole  so  finding  in  its  recognized  self- 
developement  the  unmixed  enjoyment  of  its  completed  nature, 
nothing  alien  or  foreign  would  trouble  the  harmony.  It  would 
all  have  vanished  in  that  perfected  activity  which  is  the  rest 
of  the  absolute. 

§  30.  This  crown  of  our  wishes  may  never  be  grasped.  We 
may  find  that  in  practice  it  is  not  attainable,  and  is  impossible 
for  us  to  realize  in  detail.  I  will  not  say  this  is  not  so.  Nay 
I  will  not  deny  that  this  ideal  may  itself  be  a  thing  beyond 
the  compass  of  intellect,  an  attempt  to  think  something  to 
which  thought  is  not  equal,  and  which  logic  in  part  refuses  to 
justify.  I  will  not  pass  this  sentence,  nor  will  I  gainsay  it. 
But  one  thing  I  will  say.  The  idea  may  be  a  dream,  or  even 
a  mistake,  but  it  is  not  a  mere  delusion.  For  it  does  not 
wholly  deceive  us.  It  does  set  before  us  that  which,  if  it 
were  actual,  would  satisfy  us  as  thinking  beings.  It  does 
represent  that  which,  because  it  is  absent,  serves  to  show 
imperfection  in  all  other  achievements,  takes  away  our  rest 
in  all  lesser  productions,  and  stirs  our  reason  to  a  longing 
disquiet.  There  has  come  in  to  us  here,  shut  up  within  these 
poor  logical  confines,  and  pondering  on  the  union  of  two 
abstract  functions,  a  vision  of  absolute  consummation.  In 
this  identity  of  analysis  and  synthesis  we  recognize  an  ap- 
pearance of  our  soul's  ideal,  which  in  other  shapes  and  in 
other  spheres  has  perplexed  and  gladdened  us  ;  but  which, 


Chap.  VI.]        THE   FINAL   ESSENCE   OF   REASONING.  45 1 

however  it  appear,  in  Metaphysics  or  Ethics  or  Religion  or 
^Esthetic,  is  at  bottom  the  notion  of  a  perfected  individuality. 

§  31.  We  may  seem  to  have  wandered  away  from  our 
subject,  but  in  reality,  I  think,  we  have  come  straight  upon  it. 
We  desired  to  understand  that  remaining  function,  which  fell 
outside  our  analysis  and  synthesis,  and  we  began  by  seeing 
how  far  these  principles  stopped  short  of  and  fell  outside 
completion.  Their  defect  was,  in  a  word,  the  lack  of  self- 
developement.  Is  it  an  idle  fancy,  if  we  see  in  the  element 
which  we  desired  to  understand,  and  which  passed  without 
help  from  idea  to  fact,  a  trace  of  self-developing  perfection  ? 
Or  is  it  actually  true  that  in  our  every-day  arguments  we 
must  use  an  incomplete  form  of  this  principle  ? 

We  must,  I  think,  in  the  first  place  admit  this,  that  the  act 
of  thought  by  which  we  assume  that,  given  one  possibility,  that 
one  is  real,  can  not  be  reduced  to  analysis  or  synthesis.  And 
this  act  exists  as  a  normal  function.  It  is  a  law  that,  when 
we  have  a  subject  A,  and  with  this  a  possible  predicate  b^ 
and  when  (either  because  other  predicates  are  absent,  or 
because  they  have  been  suggested  and  excluded)  this  predi- 
cate b  is  left  alone — that  then  the  subject  appropriates  this 
predicate,  and  openly  attributes  it  to  itself  as  a  possession. 
We  may  not  recognize  this  law,  we  might  even  like  to 
repudiate  its  claim,  but  we  can  not  help  obeying  it. 
Where  a  suggestion  has  been  made,  if  that  suggestion  is  not 
rejected  by  the  fact  which  we  start  with,  or  again  by  some 
other  suggested  quality,  if  in  short  we  are  left,  not  with 
disparate  possibles,  but  with  one  uncombated  may-be — that 
suggestion  must  always  be  taken  as  fact,  j  This  is  a  process  of 
thought,  and  it  does  not  seem  to  fall  under  any  previous 
process,  but  on  the  contrary  to  lie  at  the  root  of  all  our 
reasoning.  On  its  negative  side  you  may  give  it  the  form  of 
"  I  must  because  I  can  not  otherwise,"  and  you  may  reduce 
every  function  of  inference  to  this  form.  But  on  its  positive 
side,  and  that  is  the  truest,  you  may  state  it  as  "  I  must  so 
because  I  will  somehow''  The  striving  for  perfection,  the 
desire  of  the  mind  for  an  infinite  totality,  is  indeed  the  im- 
pulse which  moves  our  intellect  to  appropriate  everything 
from  which  it  is  not  forced  off. 

2  G  2 


452  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

§  32.  And,  if  I  may  guess,  it  was  this  principle  which, 
falling  from  the  sky,  appeared  disguised  as  Primitive  Credu- 
lity (Book  II.  II.  Chap.  I.  §  23).  Among  the  many  services, 
which  Professor  Bain  has  done  to  our  philosophy,  we  have  to 
thank  him  for  this,  that  he  is  incapable  of  suppressing  what 
looks  like  a  fact.  Here  in  the  middle  of  the  rest  of  his  theory, 
without  any  reasoned  connection  with  his  principles,  he  points 
out  this  seeming  irrational  readiness  to  take  ideas  as  facts,  so 
long  at  least  as  this  process  is  possible.  And  with  this,  if 
indeed  it  is  not  the  same  impulse,  goes  "  the  tendency  of  an 
idea  to  become  the  reality  "  {Senses,  p.  341).  These  primitive 
weaknesses,  according  to  our  author,  should  be  counteracted 
by  experience  and  reason,  and  are  a  thing  which  perhaps  we 
may  say  should  not  be,  and  ought  not  to  exist.  From  this 
conclusion  I  dissent,*  but  I  gratefully  acknowledge  the  frank 
acceptance  of  the  mental  tendency.  For  I  seem  to  find  in 
these  early  superstitions  a  normal  activity  of  the  developed 
soul,  the  increase  of  which  does  but  add  to  its  progress.  This 
double  effort  of  the  mind  to  enlarge  by  all  means  its  domain, 
to  widen  in  every  way  both  the  world  of  knowledge  and  the 
realm  of  practice,  shows  us  merely  two  sides  of  that  single 
impulse  to  self-realization,  which  most  of  us  are  agreed  to  find 
so  mystical.  But,  mystical  or  intelligible,  we  must  bow  to  its 
sway,  for  escape  is  impossible. 

§  33.  We  shall  hereafter  discuss  the  validity  of  this  with 
other  forms  of  reasoning,  and  we  may  here  recapitulate  our 
present  results.  Inference  is  an  experiment,  an  ideal  experi- 
ment which  gains  fresh  truth.  It  employs  divers  modes  of 
synthesis  and  analysis ;  and,  underlying  all  and  in  one  case 
apparent,  is  that  aim  of  the  intellect  after  perfect  fulness 
which  leads  it  to  appropriate  all  suggested  ideas  which  are 
not  torn  away.\  And  reasoning  depends  on  the  identity  of 
indiscernibles  ;  for  the  middle  operation  must  turn  on  a  central 
point  of  sameness,  and  again  the  datum,  with  which  we  begin, 

*  I  must  dissent  again  from  the  formula  of  Credulity,  as  given  by 
Professor  Bain,  and  which  I  have  italicized.  "  We  begin  by  believing 
everything  ;  whatever  is,  is  true^  This  at  all  events  we  can  not  believe, 
unless  we  are  idealists  of  an  extreme  type.  I  must  suppose  that  Professor 
Bain  means  "  Whatever  appears,  is  real,"  or  "  Whatever  seems,  is  /;-«<?." 


Chap.  VI.]        THE  FINAL   ESSE^XE   OF   REASONING.  453 

must  survive  through  the  process.  It  must  go  into  the 
experiment,  and  must  appropriate  the  result  which  that  ex- 
periment obtains.  We  have  seen  all  this,  and  there  is  some- 
thing else  which  now  becomes  visible.  The  identity,  which 
we  find  in  the  middle  operation,  and  the  self-preservation  of 
the  basis  we  start  with,  have  been  set  side  by  side.  But  in  a 
sense  they  really  are  one  and  the  same  ;  and  it  will  repay  us 
to  see  this.  It  shows  that  at  bottom,  and  in  a  struggling 
way,  reasoning  is  really  a  self-developement.  Throughout 
the  process  one  subject  is  developed,  and  again  to  some  extent 
it  developes  itself. 

§  34.  I  will  begin  with  the  first  of  these  assertions,  but 
will  not  weary  the  reader  with  a  repetition  of  detail.  For  the 
presumption  is  now  so  strong  in  favour  of  its  truth,  that  we 
may  content  ourselves  with  the  removal  of  obstacles.  All 
depends  on  our  looking  in  a  proper  way  at  the  premises  we 
begin  with.  If  for  instance  we  have  certain  spaces  and 
combine  them,  or  two  subjects  and  compare  them,  then  in  the 
middle  operation,  it  may  be  said,  the  unity  is  imported  from 
the  outside.  And  so  it  is,  if  you  take  the  spaces  or  the 
subjects  as  they  wrongly  appear  in  complete  independence. 
But  in  that  case  you  would  never  by  any  machinery  force 
them  together.  The  true  starting-point  is  the  total  space 
as  qualified  by  these  points  in  relation,  the  common  reality 
which  appears  in  both  subjects,  the  one  ideal  integer  in 
which  any  given  numbers  exist  as  fractions,  the  underlying 
whole  which  presents  itself  as  complex,  and  by  abstraction  is 
shown  with  a  simpler  predicate.  This  implicit  subject  is  what 
supports  the  change  brought  in  by  our  process.  And  it  also 
serves  as  a  centre  of  activity  in  the  process  itself. 

With  spaces  and  numbers  this  second  truth  is  clear.  But 
in  other  cases,  such  as  comparison,  we  may  still  verify  the 
same  rule,  f  We  begin  with  A  and  B,  and  we  compare  them  to 
find  the  relation  between  them.  But  the  centre  of  this  synthesis 
must  be  a  felt  basis  of  quality  common  to  both,  and  this  com- 
mon basis  was  implicit  in  our  starting-point.  You  may  indeed 
determine  to  compare  two  terms  before  you  know  the  special 
point  in  which  they  are  comparable  ;  but  you  can  not  perform 
the  actual  comparison,  until  the  terms  have  been  unconsciously 


454  THE   PRINCIPLES  OF   LOGIC.  [Bk.  IIL  Pt.  L 

apprehended  under  one  aspect.  Thus  reality  appears,  not 
simply  as  two  terms,  but  as  possessing  an  attribute  or  group 
of  attributes,  which  is  given  with  two  separate  sets  of  qualities. 
And  in  the  result  this  basis  through  its  own  activity  becomes 
explicit.  We  may  say  here  as  everywhere,  that  the  real  subject, 
implicit  at  the  start,  and  active  in  the  middle,  shows  itself  at 
the  end  by  a  developement  of  some  latent  relation  or  quality 
which  it  claims  as  an  attribute. 

§  35.  And  thus,  in  a  certain  sense,  the  movement  of  the 
subject  has  been  self-developement.  We  have  seen  by  how 
much  it  falls  short  of  true  freedom.  We  have  seen  how 
the  capricious  changes  which  we  effect,  and  the  external 
constructions  which  we  introduce,  stamp  the  character  of  our 
reasoning  with  an  arbitrary  print,  and  raise  painful  suspicions 
of  its  invalidity.  But  there  yet  remains  something,  which  we 
must  examine  later.  It  is  assumed  that,  whatever  in  our 
reasoning  may  be  arbitrary,  yet  at  least  the  conclusion  follows 
from  the  premises  naturally  and  necessarily,  without  altering 
or  straining  or  even  addition.  If  we  can  be  shown  of  our  own 
free  choice  to  have  forged  one  link  in  the  chain  of  inference, 
then  the  connexion  snaps  and  the  ends  fall  apart.  The 
assumption  will  trouble  us  enough  in  the  discussion  which  ends 
this  work.  But,  if  there  is  any  truth  in  it,  it  points  to  our 
belief  that  the  conclusion  must  naturally  grow  from  the 
premises,  and  can  not  in  any  way  be  dragged  or  forced  out  of 
them.  Our  apparatus  of  proof  has  been  compared  to  a 
scaffolding,  which  is  removed  when  the  edifice  of  reason  has 
been  built ;  yet,  if  we  have  but  placed  the  parts  in  conjunction, 
there  is  nothing  which  will  hold  when  the  scaffolding  is  gone. 
If  our  process  is  not  to  end  in  a  ruin,  the  apparatus  we  have 
used  must  be  simply  a  prop,  supported  on  which  the  argument 
has  grown  up,  till  strong  enough  at  last  to  support  its  own 
fruit  and  to  stand  by  itself.  Or  if  this,  as  I  fear,  is  too  high 
a  comparison,  we  may  say  that  our  constructions  must  be 
plasters  or  threads  or  splints  or  bandages,  which  hold  together 
for  a  while  our  broken  perceptions,  till  we  see  them  unite  and 
come  together.  Every  inference  we  could  make  would  prove 
unstable,  unless,  at  least  to  this  poor  extent,  it  were  self- 
developement. 


(    455     ) 


CHAPTER  VII. 

THE    BEGINNINGS   OF   INFERENCE. 

§  I.  We  have  seen  in  what  explicit  inference  consists.  It 
is  a  conscious  operation,  aware  that  the  activity  which  it 
exerts  is  ideal,  and  ending  in  a  judgment.  This  judgment 
again  is  accompanied  by  the  reflection,  that  what  went  in  at 
one  end  of  the  process,  has  come  out  at  the  other  end.  This  is 
explicit  inference,  separated,  we  shall  agree,  by  an  enormous 
interval  from  the  beginning  of  soul-life. 

It  is  not  the  purpose  of  our  volume  to  trace  the  growth 
which  in  the  end  has  bridged  this  gulf  But  we  can  not  fully 
understand  the  highest  form,  unless  we  have  at  least  given  a 
glance  at  the  lowest.  And  we  have  been  compelled  already 
in  our  account  of  judgment,  to  say  something  on  the  nature  of 
the  primitive  mind  (Book  I.  Chap.  I.  §  i8),  and  to  return  to 
that  theme,  when  we  tried  to  correct  the  vagaries  of  those 
whom  Association  has  victimized  (Book  11.  II.  Chap.  I.).  Once 
again,  and  in  the  present  Book,  the  entanglement  of  inference 
with  judgment  brought  us  face  to  face  with  the  beginnings  of 
reason.  And,  as  we  are  nearing  the  end  of  our  labours,  it 
may  be  well  to  sum  up,  and  even  to  repeat,  what  we  have  to 
say  on  the  earliest  intelligence. 

§  2.  That  intelligence  is  scarcely  to  be  recognized  ;  for  it 
lacks,  as  we  saw,  the  chief  marks  of  intellect.  It  can  not  judge, 
for  it  has  no  ideas.  It  can  not  distinguish  its  images  from 
fact,  and  so  can  not  unite  them  consciously  to  the  world  of 
reality.  And  thus  it  can  not  reason  ;  for  its  inference,  if  it  had 
one,  would  end  in  a  fact,  and  not  in  a  truth.  It  would  not  be 
aware  of  an  ideal  activity,  but  would  blindly  accept  the  trans- 
formation of  an  object.  And  even  to  this  point  it  has  not 
progressed.  As  perceived  by  the  dawning  reason,  the  object 
itself  is  unable  to  change  ;  since  if  the  change  is  to  be  known, 


456  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

the  original  must  be  retained,  and  its  sameness  held  fast. 
But  such  a  process  is  too  hard  for  nascent  intelligence.  And 
so  we  must  not  say  that  it  observes  the  fluctuation  of  the 
object,  for  it  does  not  as  yet  possess  any  object. 

I  do  not  mean  that  in  this  blurred  and  confused  totality 
there  exist  no  differences,  and  no  dim  feelings  of  self  as 
against  a  not-self;  for  these  characters,  I  believe,  are  there 
from  the  first  and  also  are  felt.  And,  if  it  were  not  so,  I  do 
not  see  how  we  could  ever  have  advanced  to  the  place  where 
we  stand.  But  these  differences,  though  felt,  are  not  for 
consciousness.  They  are  aspects  of  one  feeling,  they  are  not 
two  feelings,  in  the  sense  of  two  elements  which  present 
themselves  apart.  They  do  not  appear  as  two  realities,  for 
we  are  still  a  long  way  from  perceiving  realities.  Hence  there 
is  change  in  feeling,  not  alteration  in  things.  And,  having  no 
things,  to  repeat  it  once  more,  we  have  got  no  ideas.  And  so 
we  have  got  no  ideal  processes.  Comparison  and  distinction, 
that  bring  with  them  a  consciousness  of  agreement  and 
difference,  are  activities  we  have  not  yet  learnt  to  recognize. 
We  can  not  even  say  of  two  elements  that  they  are  like 
although  they  still  are  two.  There  is  no  memory  or  ex- 
pectation, since  the  past  and  the  future  are  nought  but  felt 
colour  and  quality  of  the  present.  And  there  is  no  world  of 
imagination  nor  play  of  fancy,  since  these  presuppose  a  know- 
ledge that  ideas  can  exist  and  be  unreal ;  while  in  the  primi- 
tive mind  no  suggestion  is  retained  which  does  not  integrate 
itself  with  felt  reality.  Dream  and  waking  again  bring  no 
known  diversity ;  for  dreams  are  not  recalled,  and  at  a  ruder 
stage  the  very  difference  seems  to  be  absent.  We  are  ever 
awake,  or  live  out  our  lives  in  a  prenatal  dream. 

We  may  say  that  at  first  the  whole  ideal  side  of  our  minds 
is  hidden  from  consciousness.  So  far  as  we  know  it,  it  is  the 
mere  dumb  feeling  of  elation  and  collapse,  which  marks  the 
continuous  flow  of  sensation. 

§  3.  So  blind  and  unintelligent  is  the  childhood  of  our 
intellect,  and  we  might  think  that  no  germ  of  intellect  was  there. 
We  might  fancy  that  we  saw  the  mere  passive  recipient  of 
external  impressions,  the  sport  of  sense  and  of  mechanical 
suggestion.     We  might  flatter  ourselves  that  at  last  we  were 


Chap.  VII.]  THE  BEGINNINGS  OF  INFERENCE.  45/ 

quit  of  activities  and  functions,  and  had  bored  too  low  for  a 
fictitious  reason  any  longer  to  trouble  us.  In  this  floating  tide 
of  presentation,  where  nothing  is  false  and  nothing  is  true, 
and  where  self-consciousness  seems  only  the  felt  practical 
relation  with  its  manifestation  of  pleasure  and  pain — we  might 
think  that  at  last  we  had  come  upon  a  soul,  which  was  free 
from  even  the  rudiment  of  those  powers  that  have  been 
ascribed  to  the  developed  intelligence. 

But,  if  we  cherished  this  thought,  we  should  fall  into  error. 
For  in  the  very  lowest  stage  of  psychical  existence  we  still  can 
point  to  a  central  activity,  and  verify  there  a  rudiment  of 
inference.  And  a  soul,  so  far  as  we  are  able  to  see,  would 
be  no  soul  at  all  if  it  had  not  this  centre.  It  would  be  an 
abstraction  which  can  flourish  in  the  heads,  and  can  take  its 
rest  on  the  shelves  of  theorists,  but  which  never  was  actual 
and  never  could  have  been  actual. 

§  4.  Physiology  gives  no  countenance  to  this  false  idea. 
It  would  be  presumptuous  for  a  layman  to  rush  in,  where 
special  education  gives  the  right  to  speak  ;  but  I  will  confine 
myself  to  a  guarded  statement.  Physiology  does  not  reject 
the  belief  that  the  beginning  of  feeling  implies  the  presence 
of  two  bodily  factors,  a  stimulus  coming  inward  from  the 
periphery,  and  then  a  reaction  on  this  from  within.*  But, 
if  so,  we  may  be  right  if  we  say  that  the  very  first  glimpse 
of  sensation  is  a  result  of  two  activities,  is  a  conclusion,  so  to 
speak,  from  two  material  premises,  of  which  the  central  response 
makes  one.  And,  if  we  considered  the  same  question  by  the 
light  of  introspection,  we  might  find  reason  to  think  that  the 
lowest  feeling,  which  we  are  able  to  observe,  does  exhibit  two 
aspects,  one  of  which  may  be  conveniently  called  .y^^-feeling.  I 
will  not  venture  to  assert  here  what  certainly  demands  a  lengthy 
discussion,  and  I  admit  that  this  double  aspect  in  sensation  is  a 
very  obscure  and  difficult  point.  But  I  thought  that  in  passing 
I  might  call  attention  to  the  fact,  that  the  mere  passivity  of 
our  first  sensations  can  be  controverted  alike  from  the  ground 
of  psychology  and  the  ground  of  physiology. 

*  I  have  purposely  used  the  vaguest  language,  as  I  do  not  feel  at 
liberty  to  assume  that  psychical  life  does  not  precede  the  developement 
of  nerves.  , 


458  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

§  5.  It  is  better  to  move  towards  plainer  issues.  Let  us 
suppose,  if  you  will,  for  the  sake  of  argument,  that  the  first 
sensation  is  a  passive  impression.  But  no  sober  writer  will 
contend  that  this  by  itself  is  experience.  The  origin  of 
experience,  we  shall  probably  be  agreed,  is  to  be  found  in  what 
is  called  reflex  action.  But  unfortunately  here  we  are  still 
in  the  region  of  doubt  and  controversy.  When  we  desire  to 
know  how  the  physical  reflex  gets  a  psychical  expression,  our 
progress  is  barred.  It  seems  not  known,  for  instance,  if  the 
efferent  side  of  the  circuit  is  ever  represented  in  consciousness, 
or,  if  it  is  represented,  how  it  comes  to  be  so.  The  so-called 
"  muscular  sense "  appears  to  be  as  doubtful  an  article  in 
physiology  as  it  is  in  psychology,  and  in  these  pages  we 
are  compelled  to  avoid  it  wholly.  And  our  only  course 
is,  I  think,  to  content  ourselves  with  an  unfavourable  view. 
Let  us  say  that  experience  begins  with  a  reflex  which  comes 
to  consciousness,  and  that,  on  the  psychical  side,  this  reflective 
circle  starts  with  a  simple  passive  sensation.  Then  follows  a 
discharge  which  moves  our  limbs,  and  brings  forth  a  change 
in  the  immediate  environment.  This  alteration  is  represented 
by  another  sensation  (however  produced),  which  for  conscious- 
ness simply  ensues  on  the  first.  From  this  modest  beginning 
we  have  to  see  how  the  activity  of  the  centre  begins  to  develope 
the  rudiment  of  inference. 

§  6.  Let  a  feeling  A  somehow  cause  a  reflex  action  y8,  with 
an  altered  feeling  C.  This  feeling  C  comes  indirectly  from 
the  reflex,  since  it  arises  from  the  change,  in  my  body  and  in 
the  object,  which  that  reflex  produces.  Suppose  now  that  a 
modified  A  recurs,  then  by  mere  reproduction  it  is  followed 
again  by  the  action  y8  ;  but  let  us  suppose  in  addition  that  ^ 
fails  in  its  former  relation  to  the  environment.  Then  C  will 
not  ensue.  The  sensation  from  the  object,  and  the  enjoyment 
of  possessing  it,  will  in  this  case  be  absent.  But  something 
else  will  be  present.  For  part  of  C  consisted  in  certain  feelings, 
arising  from  changes  in  the  muscles,  the  skin,  and  the  organs 
of  secretion.  These  changes  are  produced  once  more  by  the 
reflex ;  and  therefore,  although  the  object  is  not  there,  their 
feelings  will  come  up.  And  this  is  important :  for,  part  of  C 
coming  up,  a  redintegration  will  supply  us  with  other  parts. 


Chap.  VIL]  THE  BEGINNINGS   OF   INFERENCE.  459 

Hence,  though  the  object  is  not  present,  though  the  full 
sensation  and  pleasure  of  possession  remains  untasted,  we  yet 
are  visited  by  fainter  suggestions  out  of  harmony  with  presen- 
tation, and  that  do  not  satisfy.  This  gives  us  a  collision,  a 
contrast  between  the  new  presentation  and  the  feelings  excited 
by  the  inappropriate  reflex  action.  And  in  this  contrast  there 
lies  an  undeveloped  inference. 

We  have  not  yet  got  anticipation  baffled  and  disappointed 
hope  ;  for  the  mind  has  not  yet  reached  the  stage  of  expecta- 
tion. It  does  not  know  that  its  suggestions  are  mere  ideas. 
But,  for  all  that,  we  have  already  both  sides  of  a  process  which 
must  lead  in  the  end  to  this  great  distinction.  We  have  first 
a  modification  of  sensation  by  ideal  suggestion.  We  have 
next  a  failure  in  correspondence  and  a  collision  of  these 
elements.  And  the  pain  of  accident  or  unsatisfied  desire  will 
force  the  soul  to  consider  this  contrast,  and  to  make  explicit 
the  difference  which  it  must  feel.  Both  in  theory  and  in 
history,  it  is  mishap  and  defect  on  the  practical  side  which 
gives  birth  to  speculation. 

§  7.  For  the  early  soul-life  (it  is  a  truth  we  can  not  repeat 
too  often)  is  immersed  in  practice.  It  is  wholly  directed  to 
the  satisfaction  of  its  appetite,  first  for  food  and  then  for  the 
continuance  of  its  species.  The  selective  attention,  with  which 
it  meets  the  series  of  sensations,  is  guided  by  these  heads, 
and  is  governed  throughout  by  the  dominant  ideas  of  feasting, 
war,  love,  and  social  attachment.  For  the  sake  of  these  ideas 
it  neglects  the  main  part  of  the  offered  suggestions.  And  the 
intellect  is  so  unfree,  that  the  very  first  start  that  is  given  to 
redintegration  may  consist,  as  we  saw,  in  a  reflex  action  which 
seems  merely  physiological.  This  rule  of  the  "  passions," 
and  bondage  of  the  "  reason,"  comes  down  very  late  in  the 
scale  of  evolution,  and  it  is  hard  to  say  where  intellectual 
freedom  begins  first  to  show  itself.  The  curiosity  shown  by  the 
lower  animals,  and  their  apparent  love  for  beautiful  objects, 
are  phenomena  which  I  could  not  venture  to  interpret.  It 
seems  probable  that  pure  theoretical  curiosity  appeared  before 
man  had  been  developed  ;  though  it  no  doubt  may  be  argued 
that  the  impulse  still  remained  at  bottom  practical.  But, 
whatever   we    may  think  on  this  interesting  point,  what   is 


460  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Ft.  I. 

certain  is  this,  that  at  the  beginning  of  progress  the  intellect  is 
subordinate,  and  that  afterwards  it  becomes  at  least  partially- 
free.  And  the  conclusion  I  would  add  is,  that  the  intellect 
would  never  have  appeared  on  the  scene,  if  it  had  not  been 
present  and  active  from  the  first.  We  may  start  with  a  reflex 
that  follows  unfelt  upon  a  sensation ;  and  the  feeling  that 
ensues  may  so  far  be  taken  as  a  passive  result.  But,  together 
with  this  feeling,  are  recalled  by  a  synthesis  other  elements 
which  co-existed  with  it.  And  this  recall  has  no  immediate 
practical  link.  On  its  psychical  side  it  is  assuredly  a  rudiment 
of  intellect  and  reasoning. 

From  the  first  it  is  a  function  of  undeveloped  inference 
which  enlarges  the  given  by  ideal  suggestions.  The  selection 
of  these  suggestions  begins  with  being  practical.  There 
is,  so  to  speak,  no  attention  but  appetite.  But  gradually  the 
interest  becomes  more  remote.  It  is  held  to  appetite  by  a 
longer  chain  of  links.  And  it  possesses  at  last,  not  a  mere 
activity,  but  an  end  of  its  own.  When  this  is  accomplished 
the  reason  is  emancipated ;  and  the  history  of  the  intellect 
would  recount  the  setting  free  of  that  ideal  function  which  was 
present  from  the  first. 

§  8.  Such  a  history  would  be  hindered  by  many  difiiculties, 
and  obstacles  would  arise  upon  every  side.  It  would  find  inse- 
cure metaphysics,  one-sided  psychology,  a  physiology  in  great 
part  unsettled,  and  a  study  of  the  ruder  forms  of  the  soul  not 
long  attempted.  It  was  not  our  object  to  trace  even  the  barest 
outline  of  developement,  but  to  call  attention  to  one  cardinal 
point.  The  beginning  of  intellect,  the  first  rudiment  of  reason, 
is  present  at  the  outset  of  psychical  life.  In  what  is  called 
"association"  is  involved  the  vital  principle  of  the  highest 
logic.  For  we  must  repeat  once  more  what  we  have  insisted 
on  so  often.  Universals  are  what  operate  in  the  very  lowest 
minds.  We  may  say  the  line  of  least  resistance  is  too  narrow 
for  facts,  and  that  in  passing  they  are  stripped  and  thinned 
down  to  generals  ;  or  that  this  line,  like  our  forefathers'  ghostly 
bridge,  is  no  way  for  more  than  bodiless  spirits.  But,  however 
we  phrase  it,  the  result  remains  that  from  the  first  what  works  is 
the  universal.  It  is  never  the  whole  object,  it  is  that  in  the 
object  which  corresponds  to  the  inherited  predisposition,  which 


Chap.  VIL]  THE    BEGINNINGS   OF   INFERENCE.  461 

excites  the  reflex.  It  is  never  the  whole  feeling,  which  by 
redintegration  calls  up  those  sensations  which  accompanied 
the  past.  It  is  always  an  element  particular  to  neither,  but 
common  to  both  and  unconsciously  typical.  The  anticipated 
image  is  itself  again  an  implicit  universal ;  for  otherwise  how 
could  it  ever  be  identified  with  a  reality  not  the  same  as  itself  ? 
We  need  not  here  recall  the  detailed  discussion  which  we 
entered  on  before.  If  there  is  any  result  we  may  be  said  to 
have  established,  it  is  this,  that  from  the  first  similarity  is  not 
a  principle  which  works.  What  operates  is  identity,  and  that 
identity  is  an  universal. 

§  9.  In  the  view  which  we  take  of  the  primitive  mind  we 
have  to  battle  with  two  counterpart  mistakes.  On  the  one 
hand  we  see  in  the  lowest  life  functions  higher  than  those 
which  some  assign  to  the  highest.  The  degradation  of  the 
soul  to  an  impossible  pitch  of  decentralization  is  one  of  the- 
prejudices  against  which  we  protest.  But,  on  the  other  side, 
we  must  take  our  stand  against  the  undue  exaltation  of  early 
intellect.  With  the  most  debased  theory  of  the  beginnings  of 
the  soul  go  the  wildest  beliefs  in  the  high  capacities  of  the 
lower  animals.  Now  I  do  not  for  one  moment  profess  to  be 
able  to  fix  the  limit  reached  by  non-human  intelligence ; 
but  I  think  some  views  may  safely  be  rejected.  When 
animals,  confessedly  far  inferior  to  man,  are  represented  as 
inferring  in  a  manner  in  which  no  man  does  reason,  save  when 
working  at  hisftnost  self-conscious  level — then,  I  think,  we  may 
be  sure  that  this  idea  is  erroneous,  and  that  the  fact  must  here 
have  been  wrongly  interpreted.  We  may  perhaps  have  no  real 
knowledge,  but  still  we  have  probability. 

§  10/  We  may  illustrate  this  tendency  to  an  overhigh 
estimate  by  the  classical  instance  of  disjunctive  reasoning. 
The  dog,  who  follows  his  master's  traces,  comes  to  a  spot 
where  the  road  divides.  He  approaches  the  first  of  his  possi- 
bilities in  a  spirit  of  doubt  ;  but,  when  that  doubt  is  ejected 
by  disbelief,  his  mind  is  made  up.  He  runs  confidently  down 
the  remaining  alternative ;  for  he  has  reasoned  reflectively. 
He  is  certain  of  this  that,  if  one  has  proved  false,  the  other 
must  be  true.  But  the  instance,  I  think,  is  largely  fictitious. 
The  facts  are  uncertain  and  the  interpretation  vicious. 


462  THE   PRINCIPLES   OF  LOGIC.  [Bk.  III.  Ft.  L 

With  respect  to  the  facts,  I  venture  to  assert  that  the 
ordinary  dog  does  not  first  examine  tentatively  one  road,  and 
then  confidently  and  undoubtingly  go  down  the  other.  What 
he  visibly  does  (in  a  case  of  ignorance)  is  to  approach  both 
outlets  in  much  the  same  way  ;  or  if  he  hurries  to  the  second, 
he  does  not,  with  that  hurry,  show  any  sign  of  confidence  or 
elation.  And  the  true  interpretation  is,  I  think,  very  simple. 
When  he  comes  to  the  division  he  does  not  say,  "See  here 
are  two  ways  and  I  know  one  must  be  wrong,  I  have  therefore 
two  exclusive  alternatives."  He  does  not,  I  think,  enter  on 
these  introductory  reflections,  but  the  road  which  is  nearest 
suggests  the  idea  of  his  absent  master,  and  he  acts  on  this 
suggestion.  Then  he  fails,  and,  seeing  the  other  road,  repeats 
the  same  process,  except  so  far  as  delay  has  increased  his 
eagerness  and  hurry.  There  is  nothing  to  show  that  he  ever 
has  before  him  more  than  one  idea  at  a  single  time.  One 
suggestion  follows  and  drives  out  another,  but  different 
suggestions  are  not  held  together.  And  we  should  remember 
that  the  retention  of  an  idea,  which,  by  being  denied,  forms  the 
basis  for  a  further  positive  advance,  is  a  very  late  acquisition 
of  the  mind.  It  is  hard  to  believe  that,  where  speech  is 
undeveloped,  this  function  can  be  present. 

And,  if  I  am  told  that  from  examination  of  the  first  road 
there  are  dogs  who  will  at  once  go  down  the  other  without 
any  examination,  and  that  therefore  they  must  use  explicit 
disjunctive  reasoning — I  will  not  take  back  one  word  of  the 
foregoing.  Admitting  the  fact,  I  should  consider  the  interpre- 
tation absurd.  The  fact  to  be  explained  is  the  appearance  of 
the  last  road  as  the  path  of  the  master,  and  it  is  gratuitous  to 
explain  this  by  the  retention  of  and  reflection  from  the  negation 
of  the  residue.  It  is,  I  presume,  agreed  that  each  road  tends 
to  suggest  the  master ;  but,  if  so,  provided  only  that  the 
failure  of  the  other  roads  prevents  them  from  coming  before 
the  attention,  the  whole  fact  is  explained.  They  cease  to  be 
suggestions,  because  they  are  now  made  one  with  the  feeling 
of  failure.  They  are  hence  excluded  as  soon  as  they  are  called 
up,  and  the  remaining  suggestion  must  therefore  seem  fact  im- 
mediate and  simple.  I  have  presumed  that,  in  explaining 
the  acts  of  the  lower  animals,  we  should  not  postulate  more 


Chap.  VII.]  THE   BEGINNINGS   OF   INFERENCE.  463 

intelligence    than    is    wanted    in    order    to    account    for    the 
phenomena. 

§  II.  It  would  be  interesting,  if  it  were  possible,  to 
discuss  in  greater  detail  the  intellectual  phenomena  of  the 
primitive  soul.  But,  apart  from  other  reasons,  we  are  forced 
to  confine  ourselves  here  to  the  general,  and  may  sum  up 
what  we  have  to  say  in  these  words  :  in  the  infancy  of  reaso7t 
there  is  no  necessity.  The  nascent  intelligence  goes  to  its 
result,  not  because  of  the  premises  A  and  B,  but  because  it 
can  go  forward  in  no  other  direction.  And  even  that  is 
incorrect.  It  advances,  not  because  it  can  not  do  otherwise, 
but  because  it  advances.  The  ideal  change  takes  place 
before  it  and  is  effected  by  its  act ;  but  it  has  not  reflected 
on  the  existence  of  that  change,  and  still  less  on  its  ground. 
Thus  it  sees,  not  at  all  because  it  must  see,  but  simply 
because  it  happens  to  see.  And  for  this  reason  disjunctive 
inference  is  impossible.  There  are  no  possibilities  between 
which  to  choose,  since  every  suggestion  is  taken  as  fact  or  is 
straightway  excluded.  There  can  properly  be  no  choice 
where  the  mind  is  not  conscious  of  any  ideas.  Thought 
follows  the  line  of  the  least  resistance  ;  but  it  knows  nothing 
of  resistance  and  nothing  of  other  lines,  and  it  does  not  know 
that  it  is  even  thinking.  The  primitive  mind  has  troubles  of 
its  own,  but  as  yet  it  has  learnt  neither  its  strength  nor  its 
weakness. 

And  there  remains  an  observation  I  may  be  allowed  to 
make.  It  is  possible  that  the  upward  growth  of  the  mind  may 
so  have  changed  or  coloured  its  simplest  functions,  that  we 
can  not  any  longer  find  in  ourselves  the  psychical  phenomena 
of  the  lower  animals.  This  is  possible,  and  with  respect  to 
certain  special  functions  it  is  much  more  than  possible.  But, 
if  we  take  it  broadly,  I  confess  that  I  see  no  ground  to  accept 
it  as  probably  true.  In  the  disparaging  estimate,  if  it  is 
disparaging,  I  may  seem  to  have  formed  of  animal  intelli- 
gence, I  may  say  that  I  have  done  nothing  but  estimate  my- 
self. Without  doubting  my  own  title  to  rationality,  I  observe 
in  myself  at  my  less  conscious  moments  those  processes  and 
those  feelings  which,  with  certain  exceptions,  seem  to  explain 
the  acts  of  the  lowest  creatures.     And  these  processes  are 


4^4  THE   PRINCIPLES   OF   LOGIC.  [Bk.  IIL  Pt.  I. 

united  to  my  highest  functions  by  one  steady  advance  of  one 
single  principle,  first  unconscious,  then  reflective,  but  always 
reasonable. 

§  12.  My  excuse  for  these  poor  yet  repeated  remarks  is  on 
one  side  the  great  importance  of  the  subject,  and  on  the  other 
side  the  cloud  of  prejudice  which  darkens  it.  It  must  be 
difficult  in  any  case  to  study  the  minds  of  the  lower  animals  ; 
and  it  is  more  than  difficult  when  we  come  to  the  task  with 
false  preconceptions.  It  will  perhaps  be  no  unfitting  end  to 
this  chapter,  if  we  try  to  signalize  the  most  mischievous  of 
these. 

I  may  mention,  as  a  leading  cause  of  error,  confusion  of 
ideas  as  to  general  psychology.  An  investigator  will  discuss 
such  questions  as,  Have  dogs  got  "  self-consciousness,"  or 
Have  they  "the  power  of  abstract  reasoning,"  when  the 
approximate  meaning  of  these  terms  is  not  fixed.  Now  in 
ourselves  we  can  observe  a  number  of  stages,  beginning  with 
the  dimmest  feeling  of  self,  and  ending  with  reflective 
introspection.  It  is.  idle  then  to  argue  about  the  dog's  "  self- 
consciousness,"  when  we  have  not  tried  to  settle,  even  within 
limits,  what  the  word  is  to  stand  for.  So  again  with  the 
power  of  "abstract  reasoning."  If  we  begin  our  enquiry 
without  asking  in  what  way,  and  by  what  steps  of  develope- 
ment,  such  reasoning  is  divided  from  the  inference  which 
simply  serves  to  qualify  further  a  present  perception — how  can 
we  expect  to  go  right  in  the  end  }  One  very  great  obstacle  to 
the  study  of  animals  is  defective  psychology  propped  by  bad 
metaphysics. 

This  vitiates  interpretation,  but  observation  itself  is  largely 
vitiated.  There  is  a  tendency  in  the  lovers  of  domestic 
animals  towards  credulity  and  exaggeration.  As  we  ap- 
proach the  facts,  we  too  often  find  that  their  stories  dwindle, 
like  the  tales  of  ghosts.  And  the  tendency,  I  think,  is  not 
hard  to  account  for.  The  mere  unlikeness  of  the  other 
animals  to  ourselves  suggests  something  unknown,  and  the 
unknown  is  mysterious.  And,  besides,  there  are  powers 
possessed  by  these  animals,  which  we  do  not  possess  and 
find  hard  to  explain.  This  suggests  the  possibility  of  marvels 
without    end.      And    another   common    source    of    mistake 


Chap.  YII.]  THE    BEGINNINGS   OF   INFERENCE.  465 

co-operates.  The  observers  of  animals  too  often  forget  to 
note  the  occasions  where  stupidity  is  shown.  These  they 
pass  without  remark  and  as  a  matter  of  course ;  and  thus 
they  escape  the  difficulty  they  would  find  in  showing  how 
such  different  grades  of  intelligence  can  exist  in  one  being.* 
For,  if  you  interpret  the  successes  of  a  lower  animal  by  direct 
analogy  from  the  highest  functions  of  the  human  intellect, 
you  should  apply  the  same  principle  to  all  his  failures.  The 
total  consequence  would  be  a  strange  compound. 

§  13.  The  two  obstacles,  which  we  have  noted  so  far,  are 
a  crude  basis  of  theory  and  then  uncritical  observation.  We 
pass  from  these  to  the  doctrinal  prejudices  which  rise  from 
the  idea  of  evolution.  These  prejudices  show  themselves  in 
the  desire  on  one  side  to  minimize  the  difference  between  man 
and  beast,  and  on  the  other  side  in  the  wish  to  suppress  their 
points  of  similarity.  But,  in  each  attempt,  there  surely  is  a 
want  of  understanding.  If  we  believe  that  the  highest  has 
come  from  the  lowest  by  the  operation  throughout  of  a  single 
principle,  it  is  surely  a  derogation  from  that  principle,  when 
we  are  fain  to  help  it  by  shortening  its  course.  If  its  triumph 
is  to  pass  from  one  extreme  to  the  other,  then  by  moving  the 
goal  you  must  abridge  the  triumph.  And  again,  since  in  any 
case  the  actual  genealogy  has  not  been  recovered,  I  confess  I 
do  not  see  the  object  of  hurrying  the  historical  progress,  and 
of  straining  oneself  to  reduce  the  chain  by  some  links  at  one 
end  or  at  the  other.  We  must  agree,  I  think,  that  in  combating 
prejudice,  the  theory  of  descent  has  itself  used  prejudices. 

*  For  some  years,  while  noticing  the  habits  of  my  dogs,  I  observed 
the  views  taken  by  others  of  their  conduct,  and  was  impressed  by  the 
general  readiness  to  accept  any  kind  of  explanation,  provided  only  it 
supposed  a  high  degree  of  intellect.  In  speaking  above  of  powers  that 
we  do  not  possess,  I  mainly  allude  to  what  (perhaps  not  very  happily) 
has  been  called  the  "  sense  of  direction."  There  seems  no  ground  to 
doubt  that  some  animals  are  aware  of  distant  objects,  in  a  manner  not 
expHcable  by  smell,  vision,  or  hearing.  There  is  obviously  no  great 
antecedent  improbability  in  the  idea  that  different  animals  may  have 
diverse  senses.  And,  at  the  cost  of  a  digression,  I  should  like  to  suggest 
that  this  "  sense  of  direction,"  if  properly  established,  would  be  a  ready 
explanation  of  most  forms  of  second  sight  among  human  beings.  These 
phenomena,  if  we  suppose  them  real,  would  arise  from  the  survival  and 
abnormal  reappearance  of  a  sense  in  general  aborted. 

2    H 


4^6  THE    PRINCIPLES   OF   LOGIC.  [Bk.  III.  Ft.  I. 

But,  on  the  other  side,  what  are  we  to  say  of  our  would-be 
conservators  of  human  dignity  ?  How  can  those,  who  are  not 
slaves  to  a  childish  mythology,  persuade  themselves  that  any 
real  interest  of  their  souls  can  be  jeopardized  by  an  ape-like 
ancestor  ?  For  consider,  although  you  deny  this  parentage, 
yet  the  basis  of  your  being  is  too  plainly  animal.  Though 
more  than  a  beast,  yet,  however  you  have  come  here,  you 
assuredly  are  still  a  beast  among  beasts.  But  you  will  say, 
"  This  more,  that  divides  me  from  the  rest,  is  lost  if  my  first 
beginning  is  beast-like."  Most  foolish  rejoinder,  for  what 
do  you  fancy  is  your  own  private  history?  If  the  coming 
together  of  two  miserable  microscopical  pieces  of  matter  was 
in  any  case  your  origin,  what  worse  is  left  behind  to  destroy 
or  threaten  your  immortal  aspirations  }  If  you  do  not  blush 
to  acknowledge  the  spermatozoon,  why  scruple  to  own  the 
paternity  of  the  ape  ?  It  is  a  sensitiveness  which  seems 
irrational,  and  which  history  will  mark  as  a  ridiculous 
prejudice. 

And  it  is  the  more  ridiculous,  since  the  question  of  the 
temporal  union  of  each  soul  with  its  proper  body  was  a 
topic  for  dispute  long  before  Mr.  Darwin  fluttered  the  Church. 
It  is  hence  not  obvious  to  the  mere  stander-by  how  this 
interesting  uncertainty  about  our  ancestors  can  add  much 
material  to  the  former  dispute,  or  how  it  can  have  closed  that 
pathway  of  salvation  which,  I  presume,  the  Church  must  at 
some  time  have  found.  And,  until  we  have  some  explanation 
on  this  head,  I  think  we  must  conclude  to  one  of  two  things  : 
if  the  present  outcry  is  not  ridiculous,  the  former  calm  was 
not  very  creditable. 

But  it  is  absurd,  so  long  as  in  every  man's  history  the 
transition  has  been  made  from  the  lowest  to  the  highest, 
to  think  that  by  exaggerating  the  differences  which  exist 
between  man  and  beast,  you  tend  to  disprove  a  transition  of 
the  race  from  one  to  the  other. 

§  14.  The  prejudices,  which  up  to  this  point  we  have 
reviewed,  may  fairly  be  classed  as  intellectual  mistakes.  But 
there  remain  at  the  bottom  of  the  wish  to  disparage  and 
belittle  our  inferiors  the  threatened  hopes  of  a  privileged 
cla.ss.     What    seems   threatened    is    man's  heritage  of  a  life 


Chap.  VII.]  THE   BEGINNINGS  OF   INFERENCE.  467 

after  death.  For,  if  the  beasts  are  his  kin,  then,  since  the 
beasts  perish,  he  may  perish  with  the  beasts,  and  his  claim 
to  that  after-land  of  pure  torture  and  delight  seems  greatly 
shaken.  But,  on  this  ground  once  more,  I  confess  that  I  see 
no  just  cause  for  alarm.  And  I  would  first  recall  to  the 
orthodox  Christian  champion  of  human  nature  something  he 
may  have  forgotten.  The  new  dispensation  knows  no 
natural  claim  on  the  part  of  man  to  anything  but  un- 
pleasantness. And  hence,  if  we  can  not  hope  in  our  own 
nature,  we  can  certainly  have  no  reason  to  dread  that  nature's 
abasement. 

And  then  from  any  point  of  view  that  is  not  quite 
orthodox,  and  that  attempts  to  be  even  a  little  rational,  what 
loss  is  threatened  in  the  other  world,  if  we  admit  our  kinship 
with  the  lower  animals  t  There  are  difficulties  in  the  way  of 
their  immortality.  But  are  there  none  in  our  own  case  } 
Are  there  much  more  or  less  in  one  case  than  in  the  other  ? 
You  will  answer  perhaps,  "  I  can  not  draw  any  line  within  the 
animal  kingdom."  Will  you  draw  me  then  a  line  in  the  life 
of  a  man,  and  mark  one  period  in  his  strange  developement  as 
the  birthday  on  which  he  is  given  his  immortality }  When 
such  questions  as  these  are  once  discussed  by  daylight,  the 
answer  is  certain.  Our  relationship  to  the  beasts  would  not 
lessen  any  hope,  save  that  which  comes  from  superstition  or 
prejudice. 

§  1 5.  But,  as  we  set  ourselves  free  from  our  selfish  hopes 
and  brutalizing  fears,  we  free  ourselves  too  from  the  belief  in 
our  isolated  origin  and  destiny.  The  same  joy  in  life,  the 
same  helpless  mortality,  one  common  uncertainty  as  to 
something  beyond  draws  us  nearer  to  all  the  children  of  earth. 
The  frank  recognition  of  a  common  parentage  leaves  us  still 
the  rulers  of  our  poor  relations,  but  breaks  down  the  barrier 
which  encourages  our  cruelty,  our  disregard  for  their  miseries, 
and  contempt  for  their  love.  And,  when  this  moral  prejudice 
is  gone,  our  intellectual  prejudices  will  not  long  survive.  We 
shall  not  study  the  lower  animals  with  the  view  to  make  out  a 
case  or  a  claim,  but  for  the  pleasure  of  finding  our  own  souls 
again  in  a  different  form  ;  and  for  the  sake,  I  may  add,  of 
understanding  better  our  own  developement.     If  such  a  study 

2  H  2 


468  THE   PRINCIPLES   OF   LOGIC.  [Bk.  III.  Pt.  I. 

would  tend  on  the  whole  to  inspire  us  with  a  warranted  self- 
confidence,  it  would  call  up  some  feelings  of  self-reproach  and 
pity  and  shame. 

We  must  return  from  this  digression.  We  have  described 
the  general  nature  of  inference,  as  it  appears  in  the  special 
kinds  of  reasoning.  We  have  shown  how  the  principle 
remains  the  same  throughout  all  stages  of  psychical  evolu- 
tion. And,  while  protesting  against  the  confusion  of  these 
stages,  we  have  used  the  occasion  to  point  out  some  pre- 
judices, r  would  end  with  the  remark  that,  if  we  will  but 
keep  hold  of  and  be  in  earnest  with  the  idea  of  developement, 
we  shall  lose  all  wish  to  pull  down  the  higher  or  to  exalt  the 
lower.  We  shall  ask  throughout  for  identity  of  principle ; 
and,  above  all  things,  we  shall  not  try  to  get  that  by  diminish- 
ing the  wealth  of  varieties  and  stages  of  progress  in  which  the 
single  principle  has  found  realization. 


(     469     ) 


BOOK  III.— PART  11. 

mFERE^CE— CONTINUED. 


CHAPTER  I. 

FORMAL  AND   MATERIAL   REASONING. 

§  I.  The  words  matter  and  form  have  an  ominous  sound. 
They  tend  to  waken  echoes  from  unknown  windings  of  for- 
gotten controversy.  But  we  mean  to  be  deaf,  and  these 
murmurs  must  not  stay  us,  now  our  logical  voyage  approaches 
its  end.  We  must  neglect  the  metaphysical  questions  in 
which  these  terms  would  entangle  us,  and  even  their  logical 
bearing  we  shall  not  try  to  deal  with  exhaustively.  Nor 
again  do  we  purpose  directly  to  discuss  all  the  claims  of  the 
so-called  Formal  Logic.  Our  object  in  this  chapter  is  to 
make  such  remarks,  as  may  tend  to  clear  up  what  has  gone 
before.  And  we  hope  in  the  process  to  dispose  of  some 
prejudices,  and  finally  to  get  rid  of  some  clinging  illusions. 

§  2.  If  "  formal  reasoning  "  meant  that  we  use  a  bare  form, 
and  that  we  work  with  this,  as  it  were  with  a  tool,  on  the 
matter  of  our  premises,  this  assertion  might  very  soon  be 
dismissed.  For  we  have  no  bare  forms  we  can  so  take  in 
hand.  The  principles  of  Identity,  of  Contradiction,  and  of 
Excluded  Middle,  are  every  one  material.  Matter  is  implied 
in  their  very  essence.  For  without  a  difference,  such  as  that 
between  the  letters  A  and  B,  or  again  between  the  A  in  two 
several  positions,  you  can  not  state  or  think  of  these  principles 
(Book  I.  Chap.  V.).  And  the  nature  of  these  differences  is 
clearly  material. 

It  is  no  answer  to  object  that  the  matter  here  is  not 
special,  that  the  form  will  work  with  any  material,  and  that 


470  THE   PRINCIPLES   OF  LOGIC.  [Bk.  IIL  Pt.  IL 

the  given  material  in  each  case  does  not  formally  affect  the 
result  obtained.     It  will   not  do  to  argue  that,  since  with  all 
matter  the  identical  form  reappears  in  the  end,  and  in  every 
case  its  action  is  the  same — hence  the  matter  is  passive.    That 
would   repeat  a  fallacy  which  has  wrought  havoc  in  meta- 
physics,   and   which   in   particular    is    one    main   support   of 
Materialism.     You  can  not  conclude,  because  a  male  proves 
fertile  with  every  known  female,  that  he  therefore  supplies  the 
principle  of  fertility.     That  would  be  quite  absurd  ;  and  it  is 
always  absurd,  when  a  result  appears  from  a  pair  of  elements,  to 
argue.  Because  the  specialty  of  the  element  on  one  side  does  not 
affect  the  general  type  of  the  result,  the  other  element  is  the  sole 
cause  of  this  type.    For  something  common  to  all  the  different 
cases  may  exist  and  may  work  from  its  material  side,  and  hence 
some  matter,  after  all  may  belong  to  the  essence  of  the  formal 
activity.     The  "  bare  "  form  may  be  nothing  without  "  bare  " 
matter,  though  indifferent  to  the  varieties  of  clothing  and  colour. 
§  3.  If  formal    reasoning  means  reasoning  with  a  naked 
form,  then  it  has  no  existence.     It  is  a  sheer  illusion    and 
impossibility.      The    form,    that   we    use    as    a   principle   of 
arrangement,  is  not  form  that  can  dispense  with  every  matter, 
but  that  is  independent  of  this  or  that  special  matter.     The 
material  element,  which  remains  indispensable,  is  a  general 
quality  which  can  exist  in  any  number  of  instances.     Thus 
the  form  is  no  longer  form  absolute  but  relative. 

Now,  if  we  understand  form  in  this  relative  sense,  can 
we  say  that  reasoning  has  a  formal  character }  Or  rather 
let  us  ask  what  we  should  niean  by  such  a  statement.  We 
might  mean,  that  an  inference,  if  it  is  to  be  valid,  can 
be  shown  as  an  instance  of  a  certain  type.  We  might  mean, 
that  is,  that  the  relation,  which  is  brought  out  in  the 
conclusion,  results  from  the  relations  given  in  the  premises, 
and  that  all  these  relations  in  their  proper  connection  can  be 
anticipated  in  theory  and  reduced  to  formulas.  And  we 
might  add  that,  although  for  actual  reasoning  you  must 
possess  special  matter,  with  which  to  fill  up  the  blank  type  of 
these  formulas,  yet  this  matter  which  falls  outside  the  blanks 
is  wholly  inactive.  The  relation,  which  unites  the  terms  in 
the  end,  is  hence  not  specialized  by  the  particular  premises. 


Chap.  I.]  FORMAL  AND   MATERIAL   REASONING.  4/1 

It  is  simply  the  old  relation  of  the  formula  which,  supporting 
a  load  of  extraneous  content,  has  come  out  unaltered.  Upon 
this  view  we  may  say  that  the  type  is  a  vehicle. 

If  this  is  what  we  mean  by  reasoning  being  formal,  then  I 
will  not  say  outright  that  we  speak  of  the  impossible.  For 
by  a  stretch  of  fancy  we  perhaps  might  conceive  a  realm  in 
which  this  logic  would  be  adequate.  But  it  does  not  corre- 
spond to  real  experience.  It  is  not  merely  that  the  syllogism 
has  broken  down,  and  that  it  covers  at  its  best  but  a  portion  of 
the  subject.  It  is  that  no  possible  logic  can  supply  us  with 
schemes  of  inference.  You  may  have  classes  and  kinds  and 
examples  of  reasoning,  but  you  can  not  have  a  set  of  ex- 
haustive types.  The  conclusion  refuses  simply  to  fill  up  the 
blanks  you  have  supplied.  It  may  show  a  term  not  given  in 
the  premises.  It  may  produce  a  relation  not  anticipated  in 
the  scheme,  a  special  connection  that  arises  from  the  indi- 
vidual synthesis  of  the  elements.  And  the  attempt  to 
provide  for  these  endless  varieties  is,  as  we  have  seen  (Book  II. 
Chap.  IV.),  irrational  and  hopeless.  In  this  other  sense  of  formal 
reasoning  we  can  see  no  more  than  another  illusion,  a 
mistake  which  is  increased  if  we  confine  ourselves  to  the 
figures  of  the  syllogism,  and  aggravated  if  we  read  those 
figures  in  extension. 

§  4.  Formal  reasoning  so  far  has  turned  out  a  mere 
blunder.  Let  us  look  at  its  opposite,  and  see  what  we  can 
make  of  material  inference.  If  this  meant  that  the  conclusion 
was  really  not  got  by  work  on  the  premises,  but  required  the 
addition  of  some  other  matter,  then  of  course  it  would  not  be 
reasoning  at  all.  But  if  material  reasoning  merely  means 
such  reasoning  as  is  related  to  fact  and  refers  to  reality,  then 
this  is  an  essential  quality  and  mark  of  every  kind  of  inference. 
That  judgment  and  reasoning  could  be  confined  to  ideas  was 
an  error  which  long  ago  we  got  rid  of.  So  that  if  "  material " 
is  a  name  for  what  transcends  mere  "  concepts  "  and  commits 
itself  to  truth,  then  of  course  all  logic  must  be  material. 

But  if,  leaving  such  clear  truths  and  such  plain  mistakes, 
we  understand  our  term  in  a  different  sense,  we  may  get 
some  fresh  light  thrown  upon  the  subject.  Material  reasoning 
might  mean  such  an  inference  as  neglected  wholly  the  form  of 


4/2  THE   PRINCIPLES   OF   LOGIC.         [Bk.  IIL  Pt.  II. 

the  premises.  It  might  be  taken  in  the  sense  of  a  conclusion 
which  comes  from  the  data  when  used  in  their  full  par- 
ticularity. Given  certain  elements  in  a  particular  arrange- 
ment, it  might  be  urged  that  we  get  to  a  fresh  result,  though 
we  have  used  our  starting-point  as  this  arrangement.  The 
conclusion  has  come  from  the  whole  special  case,  and  not  by 
virtue  of  anything  it  could  have  in  common  with  another 
arrangement. 

§  5.  But,  if  we  made  this  attempt  to  rehabilitate  reasoning 
direct  from  the  particular,  we  should  once  more  end  in  failure. 
All  arguments,  as  we  saw,  fall  under  certain  heads,  and  to 
this  extent  must  forego  singularity.  But  this  is  not  all.  "  In 
every  inference  there  must  be  in  the  premises  something 
which  does  not  co-operate  in  the  work,  something  which  is 
carried  by  the  process  into  the  conclusion,  but  which  itself  is 
not  active  in  carrying  that  conclusion.  There  must  after  all  be 
in  every  argument  a  matter  which  is  not  relevant  to  its  form. 

I  do  not  mean  to  repeat  the  most  evident  truth,  that  to 
reason  from  mere  particulars  is  impossible.  That  delusion,  if 
not  dead,  for  us  is  done  with.  It  is  palpable  that,  starting 
from  sensuous  images,  you  denude  them  by  an  unconscious 
selection  and  use  them  as  types.  It  was  not  this  I  meant  ; 
but  I  wished  to  assert  that,  taking  your  premises  in  their 
proper  character,  and  reducing  them  to  that  logical  content 
which  you  really  use,  you  still  everywhere  have  something 
which  stands  to  the  form  of  the  argument  as  its  matter.  You 
have  on  the  one  side  a.4^|;ac^s  which  is  able  to  exist  with 
another  different  context.  On  the  other  side  again  you  have 
a  concrete  detail,  which  appears  in  the  basis  and  the  result, 
but  which  does  not  seem  to  contribute  a  special  character  to 
the  process.  In  this  sense  all  reasoning  is  both  material  and 
formal,  and  in  each  case  we  can  separate  the  matter  from 
/ithe  form.  We  can  find  in  each  peculiar  arrangement  an 
/iarranging  principle  which  is  not  peculiar. 

§  6.  We  should  all  admit  that  an  inference  which  did  not 
hold  in  another  example,  was  not  a  good  inference.  We 
should  agree  that  with  every  argument  there  must  always 
be  some  imaginable  case  beyond  the  present,  in  which  the 
principle  of  the  argument  would  hold.     And  we  use  this  as  a 


Chap.  I.]          FORMAL  AND   MATERIAL   REASONING.                 473  j 

'I 

test  and  trial  of  our  reasonings.     We  do  not  merely  apply  1 

the  argument  itself,  as  an  abstract  form,  to   more   concrete  ] 

instances,  with  a  view  so  to  prove  it  by  detailed  results.     We  ] 

do  more  than  this.     We  make  variations  within  the  content  j 

of  our    argument.      Thus   we   clear   the    principle   from   the  I 

matter  that  accompanies  it ;  and,  by  verifying  this  principle  j 

in  a  parallel  instance,  show  that  our  conclusion  was  not  got  ^ 

by  making  use  of  irrelevant  matter.     But  this  process  implies  \ 

a  belief  that  all  reasoning  has  a  passive  detail,  which  does  not  . 
co-operate  in  producing  the  result.                                                   ^*2r^ 

And  the  belief  is  well  founded.     In  *'  A  south  of  B,  and  C  \ 

west  of  B,  and  therefore  C  north-west  of  A,"  the  relation  of  A  • 
to  C  is  not  got  by  virtue  of  the  A  and  the  C.     These  are 

carried    by   the    spatial    interrelation,    but    they   contribute  1 

nothing  special  towards  it.     Their  differences  fall  outside  the  i 
form  of  the  argument.     Take  another  example,  "  D  =  E,  and 

E  =  F,  therefore  F  =  D."     Once   again  the  letters,  which  we  - 

use,  make  no  difference  to  their  own  arrangement.     You  must  ] 

indeed  have  some  terms  or  you  could  have  no  relations,  but  j 

the  specialty  of  these  terms  is  quite  inactive.     It  is  simple  ' 

matter   arranged  without   regard  to   its    private   claims    and  i 

peculiar  character.     If  we  take  even  such  an  abstract  instance  ; 

as  "one   and  one  =  two,"  still  here  we   can  verify  the  same  ] 

distinction.     It  may  be  said  rightly  that  the  units  are  com-  ] 

bined  to  make  the  integer,  that  the  integer  is  perceived  to  \ 

have  a  new  quality,  and  that  finally  the  identity  of  the  units  ^ 

on   both  sides  is  affirmed  in  an  equation.     And  it  may  be  ' 

further  asked,  Is  there  anything  irrelevant  in  the  whole  of  this  i 

process?     Beside  the  general  principle  of  addition  have  we  ] 

not  the  activity  of  a  special  experiment,  to  which  the  whole  of  ' 

our  datum  contributes  ?     But,  I  answer,  two  units  can  hardly  j 

be  conceived  quite  naked  and  pure.     Some  shade  of  quality,  ^ 

some  lingering  touch  of  exclusive  relation  in  time  or  space  is  % 

obscurely  present,  and   it    makes  a  difference  between  these  \ 

units  and  other  possible  units.     But,  if  so,  such  differences  \ 

will   be   immaterial   to   the   argument,  and   they  will    stand  \ 

outside   what   may   be   called   the   form.     And   in    Dialectic  \ 

reasoning  (if  we  do  not  pass  this  by)  we  shall  find  the  same  ? 

feature.     I  can  not  believe  that  the  ideas,  which  we  employ,  s 


474  THE    PRINCIPLES   OF   LOGIC.         [Bk.  IIL  Pt.  II. 

are  ever  quite  pure.  We  may  indeed  ttse  that  element  in  each 
which  is  strictly  relevant,  but  I  think  we  shall  find  that  other 
elements  are  there.  And  these  passive  diversities,  which  vary 
or  might  vary,  can  be  called  once  more  the  matter  of  the 
argument. 

If  we  had  an  inference  in  which  all  the  qualities  of  our 
content  were  active  factors  in  producing  the  result,  in  that 
case  the  matter  and  the  form  would  be  inseparable,  and  we 
could  no  longer  distinguish  them.  The  argument  would 
indeed  belong  to  a  class  more  general  than  itself,  but  its 
working  principle  would  be  confined  within  itself.  There 
would  be  nothing  that  was  passively  carried  into  the  conclu- 
sion ;  and  so,  in  this  sense,  there  would  be  no  matter. 

But  if  such  reasoning  is  an  ideal  which  we  can  never 
realize,  then  everywhere  we  may  speak  of  the  form  of  an 
argument,  as  distinct  from  its  matter. 

§  7.  Let  us  sum  up  the  result.  There  is  no  absolute 
divorce  of  matter  from  form,  but  there  remains  after  all  a 
relative  distinction.  All  reasoning  is  formal,  and  is  valid 
solely  by  virtue  of  its  form.  Every  inference  not  merely 
belongs  to  a  class,  or  a  head  of  synthesis,  but  each  has  a 
principle  which  is,  so  to  speak,  its  soul.  In  each  we  can 
distinguish  between  passive  and  active,  between  the  part  that 
carries  and  the  part  that  is  carried. 

But,  having  gone  so  far,  if  we  please  we  may  go  farther. 
Having  distinguished  we  may  separate.  We  may  extract  the 
active  principle  of  the  inference,  and  may  state  it  in  the  form  of  a 
general  axiom,  exemplified  and  instanced  in  the  actual  argu- 
ment. We  may  write  it  at  the  top  of  this  actual  arrangement, 
and  call  it,  if  we  please,  the  major  premise  (cf.  Book  II.  I. 
Chap.  IV.). 

§  8.  It  is  not  a  major  premise ;  it  is  not  any  sort  or  kind  of 
premise ;  for  it  never  has  appeared  before  the  mind.  It  is  a 
function,  not  a  datum  ;  nor  will  any  way  of  treatment  trans- 
form its  character.  The  major  premise,  we  have  seen,  is 
an  illusion  (Book  II.  Part  I.).  We  have  already  exposed 
it,  and  return  to  it  here  that  we  may  finally  show  its  root  in 
the  truth.  It  is  worth  while  to  repeat  ourselves,  if  we  only 
in  the  end  can  get  entirely  clear  of  this  obstinate  prejudice. 


Chap.  1.]  FORMAL   AND   MATERIAL   REASONING.  475 

The  defender  of  the  syllogism  may  wish  to  take  advantage 
of  our  latest  result.  If  every  inference  has  a  matter  and  form, 
then,  by  using  this  form  as  a  major  premise,  we  can  show 
every  inference  in  the  shape  of  a  syllogism.  But  this  possi- 
bility of  reduction,  he  may  urge,  is  a  proof  that  the  syllogism 
is  the  normal  type.  And  I  will  add  a  few  words  on  this 
exhausted  theme. 

In  the  first  place  I  may  remark  that  all  valid  arguments 
may  as  well  be  reduced  to  the  shape  of  equations.  If  success- 
ful torture  is  a  source  of  evidence,  then  torture  will  disprove, 
as  well  as  substantiate,  the  claims  of  the  syllogism. 

But  this  is  a  mere  argumentuin  ad  hominem  ;  and  it  is  better 
to  expose  the  root  of  the  mistake. 

§  9.  We  have  proved  that  there  are  reasonings  without  any 
major  premise.  We  have  proved  that  to  abstract  all  the 
principles  of  these  reasonings,  and  to  set  up  a  complete  and 
exhaustive  collection  is  quite  impossible.  We  have  proved 
again  that  the  principle  of  an  inference,  when  procured  and 
explicitly  stated  as  a  major,  may  be  something  quite  strange 
to  us,  that  we  do  not  recognize,  and  that  we  never  could  have 
used  as  a  premise  in  argument.  I  will  not  do  more  than  allude 
to  these  points,  which  I  think  have  been  made  evident,  and  I 
will  go  on  to  consider  the  last  defence  of  the  syllogism.  It 
may  be  said  that,  if  in  the  end  all  reasonings  will  take  this 
form,  it  must  be  in  some  sense  a  general  type. 

Let  us  consider  this  claim.  It  rests  on  the  fact  that,  having 
used  an  inference  and  obtained  a  result,  you  can  then  abstract 
the  form  of  that  inference.  You  did  not  use  this  form  as  a 
premise,  since  it  was  not  a  datum.  But  you  can  use  it,  now 
that  it  has  come  into  your  hands.  And,  so  restated,  the 
inference  after  all  will  be  a  syllogism.  This,  I  think,  is  the 
claim,  and  we  now  have  to  show  its  utter  worthlessness. 

§  10.  It  is  worthless  for  this  reason,  that  your  major,  when 
you  get  it,  may  do  no  work.  It  may  stand  above  the  actual 
process,  and  contribute  nothing  to  the  production  of  the  result. 
What  will  happen  is  this,  that  your  minor  will  contain  the 
real  operation,  and  the  major  will  be  simply  not  used  at  all. 
Let  us  take  the  inference,  "A  precedes  B,  and  B  is  con- 
temporaneous with  C,  so  that  C  must  be  later  in  time  than  A." 


476  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  IL 

We  have  to  make  this  take  the  shape  of  a  syllogism,  and  we 
do  it  by  abstracting  what  we  call  the  form.  "  What  is  prior  to 
anything  is  prior  to  that  which  co-exists  with  the  latter,"  or, 
"  When  two  events  co-exist,  and  a  third  precedes  the  first,  it 
stands  also  in  the  same  relation  with  the  second ; "  this 
becomes  the  major.  In  the  minor,  of  course,  we  have  to  bring 
the  instance  under  the  principle  ;  and  the  minor  therefore  will 
be  simply  the  whole  of  the  former  premises.  Then  what  is 
the  conclusion  .?  That  of  course  asserts  of  the  instance  in  the 
minor  the  predicate  given  in  the  major  premise.  The  predi- 
cate is  a  relation  of  antecedence  and  sequence,  which,  when 
transferred  to  the  instance,  is  the  relation  which  holds  between 
A  and  C.  And  the  result  is  undeniable  ;  it  is  certainly  correct ; 
but  then  it  does  not  result  from  the  major.  It  is  simply  the 
old  conclusion  from  the  old  premises,  which  are  now  restated  in 
the  minor.  The  minor  unassisted  did  get  out  the  result,  and  it 
is  natural  to  suppose  that  the  minor  still  continues  to  get  it ; 
while  the  major  remains  inactive  and  but  idly  presides. 

Let  me  further  explain.  We  are  offered  something  in  the 
shape  of  a  syllogism,  and  are  supposed  to  use  a  function  of 
subsumption.  Do  we  use  this  function  }  Do  we,  holding  the 
principle,  then  fill  up  the  blanks  with  A,  B,  and  C,  and  so  get 
our  conclusion  ">  Or  is  it  not  rather  true  that  we  do  precisely 
what  we  did  before,  that  is  make  a  construction  of  A,  B,  and  C, 
and  so  get  the  relation  ?  But,  if  so,  the  major  will  be  simply 
otiose.  I  do  not  say  that  its  presence  makes  no  kind  of  differ- 
ence. For  at  first  our  construction  was  not  reflective  ;  it  was 
performed  unconsciously.  And  now  we,  consciously  and  with 
some  foreknowledge  of  the  outcome,  apply  the  same  function. 
But  still  we  apply  it ;  we  do  not  cease  to  arrange  A,  B,  and  C 
in  our  minds.  We  do  not  pass  into  the  category  of  subject  and 
attribute,  and  so  get  a  predicate  A-C  by  a  mere  subsumption. 

Take  another  example.  We  have  two  pairs  of  equals,  AB 
and  BC.  By  holding  these  together  we  perceive  that  their 
quantity  is  the  same  throughout.  From  this  we  go  to  the  prin- 
ciple, "  When  two  terms  are  each  of  them  equal  to  a  third,  all 
these  terms  are  equal."  We  then  construct  a  syllogism  with  this 
axiom  as  the  major,  and  bring  out  the  old  conclusion,  A  =  C. 
But,  in  getting  this  result,  do  we  cease  to  obtain  the  relation  of 


Chap.  I.]  FORMAL   AND   MATERIAL   REASONING.  47/ 

equality  by  holding  A,  B,  and  C  together,  and  by  perceiving 
their  identity  ?  Do  we  say  "  A  and  C  are  equal  to  the  same," 
and  then,  without  any  sy7itliesis  through  B,  go  on  to  our 
conclusion  by  a  mere  subsumption  ?  Is  not  the  other  course 
more  natural,  and  is  it  not  more  rational  ?  If  we  keep  to 
those  cases  where  the  subsumption  \?, possible,  is  it  not  somewhat 
frivolous  ? 

§  II.  It  is  in  most  cases  possible.  If  you  do  not  mind 
frivolity,  you  can  torture  most  inferences  into  a  syllogism  of 
the  kind  which  we  have  just  described.  Nay,  there  are  some 
cases  where  no  torture  is  required.  For  where  an  operation 
has  been  repeatedly  performed,  the  connection  between  end 
and  beginning  grows  familiar.  We  can  dispense  at  last  with  a 
lengthy  process,  and,  using  the  axiom,  go  at  once  to  the  result 
by  a  mere  subsumption.  And  I  will  not  deny  that  the  axiom 
of  equality  may  be  so  made  use  of  But  the  subsumption  in 
these  cases  will  be  rarely  explicit.  Even  here  what  we  use 
will  not  be  a  syllogism.  Still  we  do  here  use  a  function  which, ' 
when  stated  explicitly,  would  be  syllogistic. 

In  these  cases  the  major  may  be  said  to  do  work.  The 
function  which  established  the  axiom  does  not  operate  ;  and 
the  conclusion  is  reached  by  an  act  of  recognition,  which, 
when  you  make  it  explicit,  and  so  gain  another  premise,  will 
fairly  take  the  shape  of  a  syllogism.  We  admit  that  (in  these 
cases,  which  still  are  not  syllogisms)  the  reduction  is  rational ; 
and  we  admit  again  that  in  most  other  cases  the  reduction  is 
possible,  though  utterly  frivolous. 

§  12.  But  for  all  that  the  claim  of  the  syllogism  is  worthless, 
for  the  reduction  is  not  always  even  possible.  You  must  come 
to  a  point  where  the  attempted  subsumption  proves  wholly 
illusory.  For  consider  a  regular  syllogism  itself  This  con- 
tains a  function  which  is  not  a  premise.  If  I  argue,  because 
any  man  is  mortal  and  John  is  human,  that  John  must  die,  the 
general  form  of  the  synthesis  is  not  given.  We  must  write 
the  whole  of  the  argument  as  minor  and  conclusion,  and  for 
major  we  must  take  such  an  axiom  as  "  What  falls  under  the 
condition  of  the  rule  falls  under  the  rule."  Under  this  major 
our  former  inference  is  subsumed  as  a  special  instance.  But 
now  mark  the  difficulty.     This  fresh  subsumption  is  an  active 


47^  THE    PRINCIPLES   OF   LOGIC.         [Bk.  III.  Pt.  IL 

function,  and  hence  its  principle  should  find  expression  in  a 
major.  But  what  is  this  major  ?  Suppose  we  agree  that  our 
last  axiom  was  ultimate  ;  then  once  more  this  same  axiom 
must  be  written  at  the  top,  and  it  thus  will  figure  as  the 
principle  of  itself. 

What  I  mean  is  this.  If  you  will  reduce  to  subsumption, 
in  the  end  you  must  come  to  something  final,  and  your  sub- 
sumption  will  consist  in  the  use  of  a  principle,  in  order  to 
bring  another  use  of  this  same  principle  under  itself  You 
have  first  an  argument  based  on  a  certain  function  of 
synthesis  ;  you  have  then  the  connection  of  this  argument 
with  its  function,  based  once  more  on  a  function  of  syn- 
thesis ;  and  the  first  and  the  last  of  these  functions  are 
identical.  They  are  absolutely  the  same.  But,  if  so,  I 
would  ask,  is  your  reduction  not  worthless  }  If  you  use  in 
the  end  the  precise  form  of  synthesis,  which  you  used  at  the 
beginning,  why  not  be  willing  to  stop  at  the  beginning  t  Why 
not  openly  say,  I  used  a  function  but  did  not  subsume  under  it ; 
and  my  further  reduction  has  simply  made  me  conscious  of 
what  I  did  do  t  It  has  not  changed  the  function  ;  it  has  but 
given  it  self-consciousness. 

Reduction  to  the  shape  of  a  syllogism  makes  explicit  the 
function  of  the  inference,  and  it  does  not  substitute  another 
function.  But  from  this  we  may  proceed  to  a  result  unwelcome 
to  the  friends  of  the  syllogism.  For  if  the  function  we  begin 
with  is  not  syllogistic,  we  deceive  ourselves  in  thinking  that, 
by  going  back  far  enough,  we  transmute  its  character.  Suppose 
that  A  may  be  b  and  may  be  c,  but  nothing  beyond  ;  and 
then  we  argue  from  the  absence  of  c  to  the  presence  of  b. 
This  clearly  is  not  syllogism.  But  you  say  it  is  syllogism, 
when  you  write  "  Where  I  can  not  do  otherwise  I  must,"  and 
repeat  the  inference  as  a  case  of  this  major.  Entire  delusion  ; 
for  how  is  it  that  you  know  that  your  minor  comes  under  the 
condition  of  the  major  ?  By  a  function  of  subsumption.  And 
the  principle  of  this  subsumption  is  whatever  axiom  you  agree 
to  take  as  the  basis  of  syllogism.  But  then  that  principle 
itself  is  not  so  ultimate  as  the  axiom  that  you  must  where  you 
are  unable  to  do  otherwise  ;  and  hence  it  must  stand  and  be 
based  upon   this    latter  axiom.     What  is  the  consequence  } 


Chap  I.]  FORMAL   AND   MATERIAL   REASONING.  4/9 

The  consequence  is  that  in  the  syllogism,  which  you  manu- 
facture, you  really  do  7/^^  the  more  ultimate  principle  which  you 
used  before.  But,  if  your  reasoning  actually  were  syllogistic, 
you  would  have  to  use  the  subordinate  principle.  This  would 
mean  that  the  use  of  a  higher  function  is  taken  as  the  use  of 
a  lower  function,  and  in  the  end,  if  you  carry  out  your  process, 
must  appear  as  one  case  of  a  subordinate  principle. 

§  13.  You  can  not  transmute  all  inferences  into  syllogisms 
by  extracting  their  general  function  of  synthesis.  For  that 
function,  when  exhibited  in  its  abstract  form,  continues  in 
most  cases  the  very  same  work  which  it  performed  before  ; 
and  in  some  cases  it  can  not  do  else  than  continue.  The 
difference,  which  we  have  made,  has  been  therefore  no  differ- 
ence to  the  action  itself  It  has  been  a  difference  to  our 
knowledge  of  the  action.  We  have  not  changed  the  nature  of 
our  function  ;  we  have  simply  made  a  reflection  on  that  nature. 
But,  if  so,  we  must  say  that  the  syllogism,  which  we  have 
constructed,  if  taken  as  showing  the  actual  process,  is  a 
blunder  and  mistake.  It  is  instructive  only  if  you  take  it  as  a 
mere  mode  of  reflection,  by  which  we  explicitly  state  and  lay 
down  the  function  which  we  use  apart  from  that  reflection. 

This  final  exposure  of  an  old  superstition  shows  the  root  by 
which  it  keeps  hold  of  our  minds.  There  is  in  our  arguments 
a  form  more  abstract  than  the  arguments  themselves.  And  it 
may  be  useful  to  separate  this  form  from  its  matter,  and  so 
perform  self-consciously  the  very  same  act  which  we  accom- 
plished unawares.  And  if  this  extracted  major  be  understood 
as  the  statement  of  a  principle  which  operates  in  the  minor,  and 
if  we  remember  that  it  is  the  minor,  and  the  minor  alone, 
which  in  these  cases  gets  the  concltision,  there  is  then  no  harm 
in  our  continuing  to  use  a  logical  tradition.  But,  since  we  are 
certain  not  to  remember,  and  since  others  (if  we  remember)  will 
forget,  my  voice,  if  I  have  one,  is  for  putting  under  ground 
this  much  decayed  object  of  unpleasant  warfare. 

§  14.  Let  us  cease  to  pretend  that  the  principle  is  a 
premise.  Let  us  try  to  call  things  by  their  real  names  ;  and, 
instead  of  applying  for  the  production  of  a  major,  simply  ask 
for  the  form  and  principle  of  an  argument.  This  is  rational 
and  useful ;  it  is  good  alike  for  theory  and  for  practice.     By 


480  THE    PRINCIPLES   OF   LOGIC.         [Bk.  III.  Pt.  IL 

finding  the  functions  made  use  of  in  our  proofs,  we  can  classify 
them  with  a  view  to  a  further  understanding.  And  we  may 
thus  avoid  some  mistakes  in  the  actual  work  of  reasoning. 
For  by  an  exhibition  of  the  abstract  principle  we  can  dis- 
tinguish what  is  relevant  from  irrelevant  detail.  When  doubt- 
ful of  an  inference  we  may  desire  to  know  how  the  conclusion 
is  got.  We  therefore  ask  for  the  active  function,  and  we  make 
this  explicit,  by  direct  abstraction  from  the  inference  in  hand, 
or  indirectly  by  a  previous  comparison  with  other  instances. 
In  this  way  we  can  test  the  form,  either  by  a  simple  scrutiny 
of  itself,  or  by  seeing  how  it  works  in  fresh  applications  and 
further  deductions.  And  this  process  is  useful  as  well  as 
rational. 

§  15.  There  are  two  parallel  mistakes,  which  we  must  try 
to  avoid.  We  must  not  fall  into  thinking  that  our  actual 
inferences  are  proved  by  deduction  from  a  general  form. 
And  we  must  shun  the  idea  that  this  principle  itself  is  proved 
by  the  collection  of  working  examples.  The  universal  neither 
demonstrates,  nor  is  demonstrated  by,  its  particular  appli- 
cations. 

It  does  not  demonstrate  them  for  this  reason.  It  is  not 
a  statement  which  is  believed  when  received,  but  a  function 
which  must  be  worked  in  order  to  be  seen.  And  it  can  not 
be  worked  quite  pure  in  a  vacuum.  Some  matter  must  be 
used.  And  hence,  when  we  lay  down  the  abstract  principle 
we  really  are  using  a  concrete  instance,  though  we  distinguish 
in  that  instance  the  matter  from  the  form.  But  this  shows 
that  in  the  end  our  criterion  must  be  an  individual  ope- 
ration. 

Take  for  instance  the  axiom,  that  things  equal  to  the  same 
are  equal  to  each  other.  The  only  method  of  perceiving  this 
general  truth  is  to  make  an  experiment  in  which  you  distinguish 
the  equality  from  the  other  attributes  of  the  terms,  and  observe 
what  each  element  contributes  to  the  result.  We  must  use  in 
the  end  this  individual  test. 

"  But,"  it  will  be  said,  "  this  criterion  in  its  use  is  universal, 
and  our  particular  reasonings  are  proved  by  subsumption 
under  its  conditions."  This  is  the  old  mistake.  Our  fresh 
cases,  as  we  saw,  are  themselves  proved  true  by  a  renewed 


Chap.  L]  FORMAL   AND   MATERIAL   REASONING.  48 1 

experiment.  Our  criterion  serves  merely  to  show  us  the 
essence  of  the  act  which  we  perform,  and  to  give  us  in  the 
operation  the  distinction  between  its  form  and  matter.  But 
the  consciousness  of  this  distinction,  I  must  repeat,  is  not  the 
proof  of  the  actual  conclusion.  You  might  just  as  well  say- 
that  the  fresh  use  of  the  function  was  a  proof  of  the  axiom. 

§  16.  And  this  last  remark  leads  us  to  the  parallel  mistake. 
No  amount  of  mere  instances,  where  the  function  is  used,  would 
demonstrate  its  principle.  Their  number  and  their  variety- 
are  precisely  that  part  of  them  which  is  not  relevant  to  the 
principle  itself  When  operations,  that  look  like  analogous 
instances,  all  have  consequences  which  square  with  the  nature 
of  things,  this  affords  a  presumption  that  some  valid  principle 
is  present  though  unknown.  But  the  proof  of  this  principle 
comes  solely  from  abstraction ;  and  the  number  and  the 
differences  of  our  applications  help  us  only  so  far  as  they  help 
us  to  this  goal.  They  work  not  by  the  support  but  by  the 
destruction  of  each  other.  They  prove  the  axiom  by  dis- 
carding themselves,  and  they  all  unite  to  demonstrate  each 
by  reciprocally  discounting  their  private  irrelevancies. 

We  may  so  put  the  result.  A  principle  will  neither 
demonstrate  its  applications,  nor  can  it  be  demonstrated  by 
them.  The  principle  is  demonstrated  when  we  see  it  in,  and  as 
the  function  of,  an  individual  act.  The  instance  is  demonstrated, 
first  by  the  concrete  performance  of  the  function  ;  and  secondly 
it  is  shown  to  be  an  instance,  when  in  that  performance  we 
distinguish  the  form  from  the  passive  matter. 

§  17.  You  can  not  reduce  all  reasoning  to  syllogism. 
Every  inference  is  necessary,  and  the  necessity  of  the  process 
can  be  formulated  as  an  universal  truth.  This  principle  is 
more  abstract  than  the  inference  itself,  and  more  abstract  than 
the  conclusion  which  the  inference  reaches.  But  then  itself 
is  not  one  of  the  premises.  It  is  that  which  developes  the 
conclusion  from  the  given,  but  it  is  not  given  itself;  and  the 
attempt,  as  we  saw,  to  get  it  into  the  given,  conducts  us  to 
a  process  that  is  simply  idle.  It  is  this  confusion  between 
principle  and  premise  which  has  served  to  protect  the  old 
age  of  the  syllogism. 

And  on  this  basis  we  saw  that  we  might  effect  an  under- 

2  I 


482  THE   PRINCIPLES   OF   LOGIC.         [Bk.  III.  Pt.  II. 

standing.  If  it  were  admitted,  on  one  side,  that  the  syllogism 
supplies  no  general  type  of  the  reasoning  act,  it  might  be 
allowed,  on  the  other  side,  that  it  is  a  mode  of  stating  the 
principle  which  is  used  in  that  act.  It  is  universal  as  a  form 
for  showing  the  explicit  and  conscious  exercise  of  a  function. 

But,  for  myself,  I  must  repeat  that,  friendly  as  I  am  to  the 
friends  of  the  syllogism,  I  can  not  venture  to  support  this 
compromise.  When  I  think  of  the  futile  and  fatuous  perfor- 
mances enjoined  upon  the  student,  when  I  think  of  the  nature 
of  too  many  of  his  instructors,  I  feel  sure  that  the  syllogism, 
if  it  continues  to  be  taught,  will  be  taught  as  a  form  to  which 
we  must  reduce  every  valid  argument.  It  would  never  be 
taught  as  a  form  in  which  we  may  state  our  knowledge  of  an 
argument's  principle.  And  then,  even  if  the  orthodox  logic 
might  be  learnt  in  this  heterodox  spirit,  we  should  cover  in  the 
end  but  a  part  of  our  subject.  I  can  not  speak  from  experience 
of  the  more  active  side  in  the  educational  suffering,  but  still  I 
must  venture  to  offer  a  suggestion.  Most  humbly  I  would 
submit  to  all  teachers  who  are  resolved  to  stand  by  the  syllo- 
gism, that  they  are  teaching  what  is  either  incomplete  or  false. 
And  if  they  care  not  for  truth  but  for  practical  results,  then  I 
think  for  the  sake  of  their  much-enduring  pupils  they  are  bound 
to  make  at  least  some  trial  of  the  Equational  Logic.  There  is 
reason  to  think  that  it  might  answer  better,  and  I  hardly  see 
how  it  could  turn  out  much  worse. 

§  1 8.  We  have  now  finished  all  that  we  desired  to  say  on 
the  relation  of  matter  to  form  in  logic.  We  have  seen  that  no 
reasoning  is  absolutely  formal,  but  that  141  logic,  as  indeed  in 
all  other  sciences,  there  is  a  relative  distinction  of  form  and 
matter.  We  then  entered  a  repeated  and  final  protest  against 
the  idea  that  action  was  subsumption  under  a  form  of  activity. 
And  we  expressed,  not  a  hope,  but  a  pious  wish  that  together 
with  this  false  notion  the  syllogism  might  be  banished. 

We  may  end  these  inadequate  remarks  by  a  warning,  that 
both  matter  and  form  bear  other  senses,  which  we  have  not 
mentioned.  An  inference  may  be  good  in  point  of  form,  when, 
though  the  substance  is  incorrect,  the  conclusion  follows  from 
the  premises  given.  An  argument  again  is  formal,  when  its 
steps  are  drawn  out  in  regular  detail ;  or,  possibly,  when  the 


Chap.  L]  FORMAL   AND   MATERIAL   REASONING.  483 

principle  is  explicitly  stated.  Substantial  again  or  material 
may  mean  much  the  same  as  implicit.  A  process  once  more 
is  merely  formal,  when  it  effects  an  arrangement  which  is  not 
material  to  the  substance  of  the  case.  But,  where  the  form  is 
the  essence,  mere  material  alteration  is  likewise  irrelevant.  The 
further  question  how  the  form  stands  to  the  universal,  turns 
upon  the  categories  of  relation  and  quality,  and  can  hardly  be 
discussed  outside  Metaphysic.  And  with  these  disjointed 
statements  we  must  pass  to  a  theme  which  has  long  been 
awaiting  us. 


2  I  2 


484  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Ft.  IL 


CHAPTER  IL 

THE  CAUSE  AND  THE  BECAUSE. 

§  I.  We  have  seen  that  an  inference  is  an  ideal  operation 
which  gives  us  a  result.  The  conclusion  comes  because  of  the 
process,  and  it  is  natural  to  imagine  that  the  process  must 
therefore  answer  to  the  cause.  If  so,  we  should  be  led  by  a 
very  short  cut  to  a  far-lying  goal.  In  reasoning  we  should 
always  be  knowing  by  causes,  and,  at  least  for  our  knowledge, 
the  connection  of  truths  and  the  course  of  events  would  be  one 
and  the  same.  But  such  a  rapid  success  is  itself  enough  to 
awaken  suspicion.  Great  results  in  metaphysics  are  not 
reached  so  easily,  and  a  promise  of  short  ways  is  almost 
sure  to  conduct  us  into  error.  We  should  find  that  enquiry 
would  confirm  the  doubt  excited  in  our  mind  by  this  general 
presumption. 

Is  the  middle  in  reasoning  always  the  cause  }  No  doubt 
we  have  some  ground  for  taking  this  as  true.  For  wherever 
we  say  "  because,"  there  must  be  an  inference.  Wherever  we 
ask  "  why,"  we  ask  for  a  reason  ;  and  a  reason,  when  given,  is 
once  more  a  because.  And  so  we  might  conclude,  since  to 
infer  is  to  reason,  and  since  in  reasoning  we  always  make  use 
of  a  reason  which  gets  the  result,  that  the  middle  in  an 
argument  represents  the  cause,  and  that  the  conclusion  stands 
for  the  effect  of  the  premises. 

§  2.  It  would  be  irrational  either  to  affirm  or  to  deny  such 
a  general  assertion.  For  we  can  not  say  at  once  what  it 
signifies.  The  word  "cause,"  we  know,  has  a  great  many 
meanings ;  and  its  ambiguity  does  not  lie  in  mere  verbal 
looseness,  or  rest  on  the  chance  obscurities  of  language.  It  is 
the  cloud  that  arises  round  the  common  source  of  many  great 
problems  ;  and,  if  we  tried  to  penetrate,  we  should  at  once  be 
lost  in  the  mist  of  metaphysics.     The  "cause"  may  not  be 


Chap.  II.]  THE   CAUSE  AND   THE   BECAUSE.  485 

distinguished  from  the  "  principle,"  and  then  every  universal 
connection  will  be  a  cause.  On  the  other  hand  "cause" 
tends  to  pass  into  "  substance."  It  appears  again  as  "  energy," 
"force,"  and  "power,"  accepted  by  some  as  the  essence  of 
reality,  while  rejected  by  others  as  absolute  illusion.  The 
controversy,  that  springs  from  this  radical  difference,  would  be 
fought  over  the  fields  alike  of  metaphysics,  psychology,  and 
physiology,  and  would  embroil  us  everywhere  in  debate  and 
uncertainty.  We  should  ask  in  vain  for  any  harmonious 
finding  as  to  the  bodily  process  which  conditions  my  feeling 
of  energy  put  forth.  We  should  find  no  answer  if  we  desired 
to  know  the  actual  deliverance  of  consciousness  itself,  and 
begged  for  an  account  of  what  we  feel  as  will.  And  lastly, 
when  we  enquired  if  Force  or  Energy  is  anything  conceivable, 
if  it  is  an  idea  self-consistent  and  so  far  possible,  or  a  coarse 
delusion  that  breaks  up  before  scrutiny — we  should  receive 
once  more  conflicting  responses. 

If  we  mean  to  ask  here  how  the  grounds  of  our  reasoning 
stand  to  the  causes  of  our  real  events,  we  must  begin  by 
limiting  the  meaning  of  our  term.  Cause  must  be  confined 
to  the  antecedent  member  within  a  law  of  the  sequence  of 
phenomena.  I  do  not  mean  that  the  cause  is  to  be  the 
unvaried  event,  that  it  is  something  which,  throughout  a 
collection  of  instances,  has  happened  in  time  before  something 
else.  We  must  take  it  in  the  sense  of  the  invariable  event. 
It  is  that  to  which,  supposing  that  it  happens,  something  else 
will  succeed.  In  other  words  it  is  the  hypothetical  datimi  from 
which  there  comes  a  necessary  consequence.  It  is  an  universal 
element  in  an  ideal  law  of  the  sequence  of  phenomena.* 
(Cf  Book  I.  Chap.  II.) 

*  The  term  "  unconditional "  would  merely  express  this  same  idea. 
If  B  comes  invariably  from  A,  it  must  come  unconditionally ;  for  the 
introduction  of  a  condition  would  modify  A,  so  that  B  would  no  longer 
come  from  //.  And  again,  supposing  that  we  could  say  no  more  than 
that  "  B  follows  from  A,  when  A  is  conditioned,"  I  do  not  see  hqw  in 
that  case  we  could  assert  that  B  follows  invariably  from  A.  We  could 
not  assume  that  an  alteration  of  the  conditions  is  impossible,  or  that  no 
possible  alteration  would  affect  the  sequence.  I  do  not  ask  if  the  know- 
ledge of  the  invariable  and  unconditional  is  possible  in  fact.  Cf  §  14, 
and /w/rrt:  Chap.  III.  §  II.  . 


486  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  II. 

§  3.  If  by  cause  we  understand  the  antecedent  in  a  law  of 
the  succession  of  phenomena,  we  can  at  once  proceed  to 
discuss  the  question,  Are  the  cause  and  the  reason  always  the 
same  ?  And  we  may  divide  the  enquiry  into  these  two  parts, 
(i)  Is  the  cause,  as  we  know  it,  always  a  because  ?  (ii)  Does 
every  because  appear  as  a  cause  ? 

(i)  Is  causation,  in  the  first  place,  known  by  inference  } 
Can  we  say  there  is  a  cause,  when  we  do  not  reason  }  This 
would  surely  be  impossible ;  for,  in  perceiving  the  cause,  we 
must  perceive  the  law,  and,  possessing  the  law,  we  have  at 
once  in  our  hands  an  universal  connection.  And  to  judge. 
Here  is  a  cause,  is  to  take  the  antecedent  as  an  instance  of 
this  law,  and  to  take  the  result  as  a  necessary  consequence. 
But  this  process  is  reasoning. 

It  is  useless  to  deny  it.  It  may  be  said  that  the  actual 
process  of  causation  is  a  real  chain  of  existing  things,  and  is 
no  ideal  construction  formed  by  our  minds.  But  this  objection, 
if  true,  would  be  quite  irrelevant ;  for  we  are  talking  of  cause 
and  effect  as  we  know  them.  And  without  such  a  reconstruc- 
tion it  is  impossible  to  know  them. 

§  4.  I  may  be  told  that  the  cause  and  the  effect  are 
presented,  that  they  are  given  to  sense.  Well,  for  argument's 
sake  let  us  suppose  that  the  sequence  is  confined  to  a  single 
sense-perception.  It  does  not  follow  from  this  that  our  senses 
present  it  to  us.  We  surely  never  could  see  that  mere  B  follows 
mere  A.  We  see  a  complex,  a  tangle  of  details,  from  which 
we  separate  this  thread  of  succession.  The  so-called  fact,  that 
mere  A  comes  immediately  in  time  before  B,  is  an  universal 
connection,  which  is  reached  by  a  process  of  intellectual 
abstraction.  Itself  is  ideal ;  it  is  nothing  that  -by  any 
possibility  could  exist.  For  A  is  not  a  phenomenon,  nor  is 
B  a  phenomenon,  but  both  are  abstractions.  Their  relation 
again  is  no  phenomenal  sequence.  It  is  purified  from  a  mass 
of  irrelevant  details,  it  is  removed  from  the  flux  of  actual 
events.  It  is  a  truth  that  is  true,  not  anywhere  but  in  the 
region  of  universals  and  the  world  of  hypothetical.  And  the 
result  of  this  is  that  to  know  the  law  is  to  know  the  product  of 
a  reasoning  by  abstraction  ;  to  know  the  instance  is  to  recon- 
struct this  case  as  a  synthesis  of  the  law  with  a  particular 


Chap.  II.]  THE   CAUSE   AND   THE   BECAUSE.  48;^ 

element ;  and  to  know  the  so-called  particular  fact,  that  A 
comes  before  B,  is  either  to  perceive  something  which  in  part 
has  no  connection  with  the  mere  and  pure  antecedence  of  A  to 
B,  or  else  must  be  really  in  a  particular  instance  to  apprehend 
the  very  law  itself     (Cf  Book  I.  Chap.  II.) 

For  example,  if  I  see  a  man  fire  at  an  animal  and  say,  The 
shot  was  the  cause  of  death — the  cause  is  here  clearly  a  because 
and  a  reason.  For  I  have  isolated  this  thread  from  the 
sequence  of  phenomena,  and  now  unconsciously  take  the 
particular  fact  as  an  instance  and  application.  Thus  let  the 
whole  act  of  firing  be  A  {cde),  and  the  fall  of  the  animal  be 
B  {fgJi) ;  the  apprehended  connection  will  be  A  —  B,  and  it  is 
because  we  perceive  this  that  we  are  able  to  say,  A  {cde)  and 
tJierefore  B  {fgJi).  The  inference  is  probably  not  explicit,  but 
it  certainly  is  there.  For  how  could  I  tise  the  observed 
succession  in  other  cases,  if  it  was  not  universal }  And  how  in 
this  case  could  I  speak  of  causation,  as  distinct  from  mere 
succession,  if  I  did  not  take  this  sequence  as  having  a 
principle  which  connects  its  terms  ?  But  that  is  reasoning  and 
inference. 

§  5.  Causation  is  no  mere  phenomenal  sequence.  It  implies 
a  principle  felt  in  the  succession  of  the  elements  ;  and  that 
principle  is  a  connection  which  can  not  be  presented.  Let  us 
dwell  on  this  truth.  We  have  seen  that  it  holds  with  a  simple 
succession,  but  it  holds  still  more  with  a  true  process  of 
causation  ;  for  that  (if  we  go  on  to  understand  it  rightly)  can 
not  possibly  be  a  simple  relation  of  sequence.  It  is  a  change 
in  time,  and  no  change  would  take  place  unless  it  arose  from 
a  meeting  of  elements.  To  apprehend  causation  we  must  first 
distinguish  the  elements,  before  they  have  come  together. 
And  thus  we  get  to  perceive  what  may  be  called  the  "  con- 
ditions "  (p.  195).  But  these  conditions,  when  asunder,  are  not 
yet  the  cause.  To  make  the  cause  they  must  come  together  ; 
and  their  union  must  set  up  that  process  of  change  which,  when 
fixed  artificially,  we  call  the  effect.  Hence  to  know  causation 
we  must  {a)  first  have  the  elements  in  ideal  separation ;  we 
must  iU)  then  ideally  reconstruct  their  meeting,  and  from  that 
{c)  perceive  the  issuing  change.  But  such  a  knowledge  surely 
can  not  come  from  presentation. 


488  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  II. 

To  repeat — you  can  not  properly  talk  of  causation,  unless 
you  can  say  first  that  something  was,  then  that  something 
happened  to  it,  and  that  so  something  else  appeared  in  time. 
The  full  "  conditions  "  are  not  the  elements  apart,  but  the 
elements  together  with  the  change  which  unites  them,  and 
combines  itself  with  them.  It  is  in  the  moment  when  this 
union  is  realized,  that  the  process  begins  ;  for  otherwise  the 
"  cause  "  might  exist  for  ever,  and  not  begin  to  produce  its 
effect.  But  this  process  of  change  is  itself  the  effect,  and 
nothing  else  can  in  strictness  have  a  right  to  that  name.  We 
have  first  the  elements  apart,  then  their  union,  and  lastly  the 
product*  You  can  not  even  think  the  law  of  your  instance 
without  an  ideal  synthesis  through  identity. 

Thus  to  experience  a  definite  relation  of  succession  de- 
mands the  separation  of  irrelevant  and  relevant.  But  this  is 
abstraction,  and  therefore  inference.     And  to  experience  that 

*  Hence  we  see  that  a  cause  demands  previous  change.  It  can  not 
exist  without  producing  its  effect,  so  that,  if  the  effect  is  to  have  a  begin- 
ning, the  cause  must  have  a  beginning  also.  To  produce  the  effect  it 
becomes  the  cause  ;  and  that  becoming  is  a  change  in  time,  which  natu- 
rally calls  for  another  cause  by  which  to  account  for  it.  Yitxizt first  cause 
is  pure  nonsense. 

Again  the  effect  is  the  change  which  issues  from  the  union  of  the 
conditions.  It  is  a  passing  event,  and  it  is  only  by  a  Hcence  that  we 
allow  ourselves  to  treat  it  as  a  permanent  product.  Being  a  phenomenon 
in  time  it  can  not  persist.  Once  more  the  effect  must  follow  the  con- 
stitution of  the  cause  ;  it  can  not  begin  until  after  the  moment  when  the 
synthesis  is  complete.  It  is  impossible  it  should  ever  co-exist  with  its 
cause,  and  the  belief  that  it  does  so  arises  from  confusion.  For  we  forget 
that  both  cause  and  effect  are  events,  and  we  tend  to  think  of  them  as 
substances  maintaining  an  identity  in  spite  of  events. 

But,  though  the  effect  succeeds,  it  succeeds  iiti7nediately.  Causation 
is  really  the  ideal  reconstruction  of  a  continuous  process  of  change  in 
time.  Between  the  coming  together  of  the  separate  conditions  and  the 
beginning  of  the  process,  is  no  halt  or  interval.  Cause  and  effect  are 
not  divided  by  time  in  the  sense  of  duration  or  lapse  or  interspace. 
They  are  separated  in  time  by  an  ideal  line  which  we  draw  across  the 
indivisible  process.  For  if  the  cause  remained  for  the  fraction  of  a 
second,  it  might  remain  through  an  indefinite  future.  Permanent  cause, 
unless  you  take  cause  in  another  meaning  and  treat  it  as  substance,  is 
simply  nonsensical  I  should  be  glad  to  discuss  some  of  the  difficulties 
which  arise  in  connection  with  causation,  but  the  questions  raised  would 
hardly  be  logical. 


Chap.  II.]  THE  CAUSE  AND  THE  BECAUSE.  489 

succession  as  following  a  change  implies  a  reconstruction  by- 
identity  and  a  further  inference.  But  the  main  point  is  this. 
To  recognize  a  succession  as  a  causal  sequence  means  to  perceive 
the  facts  as  a  presented  law.  And  to  see  the  law  in  the  facts  is 
to  unite  the  facts  by  an  ideal  principle  ;  and  this  is  to  reason. 
In  other  words  to  say,  This  phenomenon  B  was  the  effect  of  A, 
implies  the  perception  of  an  ideal  connection  between  A  and  B. 
But  to  know  by  means  of  an  ideal  connection  is  to  know  that 
the  fact  is  a  result  of  that  connection.  And  this  must  be  in- 
ference. It  may  be  latent  and  unconscious,  yet  still  it  is  there. 
The  mere  conjunction  has  become  a  connection,  felt  as  such. 
And  this  connection  is  now  used  with  other  conjunctions.  But, 
if  so,  the  facts  are  united  in  my  mind  because  of  an  universal. 
§  6.  The  thread  of  causation  is  nothing  visible.  It  is  not 
seen  till  it  is  demonstrated  ;  and  it  is  demonstrated  solely  by  the 
ideal  decomposition  and  reconstruction  of  events.  It  is  an  ideal 
unity  which  we  discover  and  make  within  the  phenomenal 
flux  of  the  given.  But  it  has  no  actual  existence  within  that 
flux,  but  lives  first  within  the  world  of  universals. 

And  from  this  we  may  proceed  to  draw  a  consequence 
which  serves  to  transform  a  worn-out  controversy.  To  ask  if 
the  belief  in  cause  and  effect  results  from  the  mere  repetition 
of  sequences,  is  to  put  the  question  in  a  form  which  ensures 
and  necessitates  an  erroneous  answer.  For,  if  the  definite 
sequence  has  once  been  perceived,  what  need  can  there  be  for 
further  repetition  }  The  knowledge  that  mere  B  has  followed 
on  mere  A,  would  itself  be  the  very  goal  which  we  desire 
to  reach.  But  on  the  other  hand  if  this  pure  sequence  is 
never  experienced  by  mere  sense-perception,  then,  with  all  our 
repetition  of  innumerable  perceptions,  we  do  not  ever  repeat 
the  experience  of  that  sequence.  The  true  point  at  issue  is 
the  way  in  which,  from  impure  presentations,  we  derive  the 
pure  intellectual  sequence  of  B  from  A.  And  we  have  seen 
that  the  process  is  in  principle  abstraction,  and  in  its  essence 
consists  of  ideal  analysis.  The  repetition  serves  merely  as  a 
helftto  the  abstraction  (Chap.  I.  p.  480). 

§  7.  Since  to  recognize  a  case  of  cause  and  effect,  is  to 
apprehend  the  instance  of  a  law  universal,  and  which  can  not 
be  presented  in  sense  perception,. we  are  safe  in  saying  that, 


490  .  THE   PRINCIPLES  OF   LOGIC.        [Bk.  IIL  Pt.  II. 

in  order  to  know  causation,  we  are  forced  to  reason.  And  in 
this  connection  we  may  perhaps  be  excused,  if  we  pause  to 
consider  a  radical  mistake.  Reasoning,  we  are  told,  consists 
in  a  seeing  with  the  eye  of  the  mind,  by  which  we  perceive 
"  details  now  unapparent  to  sense."  It  is  "  a  mental  vision 
reinstating  unapparent  details."  "  What  is  termed  the  ex- 
planation of  a  phenomenon  by  the  discovery  of  its  cause,  is 
simply  the  completion  of  its  description  by  the  disclosure  of 
some  intermediate  details  which  had  escaped  observation."  * 
It  would  be  difficult  to  find  any  statement  more  opposed  to 
the  doctrine  which  we  embrace. 

And  it  is  a  statement  which  collapses  before  the  smallest 
scrutiny.  For  suppose  the  whole  mass  of  djkail  to  be 
present,  suppose  not  the  smallest  element  to  fail — is  this 
huge  congeries  an  explanation  }  Or  what  is  explanation  ? 
Does  it  not  rather  consist  in  finding  within  this  mass  the 
threads  of  connection .?  But  these  threads  are  no  details,  and 
they  unite  no  details,  apparent  or  unapparent.  For  they  are 
made  by  abstraction,  by  a  getting  away,  from  {he  details  of 
sense  and  their  sensuous  relations,  to  universal  laws  which 
subsist  between  elements  too  pure  to  be  presented.  The 
sequences  of  science  may  be  got  by  observation,  and  may  be 
given  by  description ;  but  it  is  an  observation  which  mutilates 
phenomena,  and  a  description  which  shears  off  all  those 
details  which  belong  to  the  very  essence  of  presentation. 

§  8.  To  explain  a  fact  you  must  exhibit  it  as  the  instance 
of  a  general  principle  or  meeting  of  principles.  The  mere 
beholding  an  intermediate  something  would  be  dy  itself  no 
kind  of  explanation.  It  is  an  old  superstition  to  look  for 
causality  in  a  something  coming  between  the  first  fact  and  the 
second  one.  You  can  explain  without  any  sort  of  inter- 
mediate, and,  when  you  have  intermediates,  you  may  still 
have  not  explained. 

I  am  far  from  wishing  to  write  down  these  platitudes,  but 
they  may  serve  to  dispel  a  thoughtless  mistake.  Suppose 
that  I  place  a  glass  bottle  on  the  fire  and  it  presently  breaks. 

*  G.  H.  Lewes,  Aristotle^  p.  76.  I  do  not  raise  the  question  how  far 
Mr.  Lcwes's  later  (and,  I  presume,  borrowed)  utterances  are  consistent 
with  this  view.     It  is  a  typical  mistake,  and  as  such  may  be  examined. 


Chap.  II.]  THE  CAUSE   AND   THE   BECAUSE.  49I 

"  If  you  had  better  eyes,"  I  shall  hear  the  remark,  "  you 
would  see  the  molecules,  and  see  them  irregularly  increasing 
their  distance  the  one  from  the  other.  Then  the  bottle  would 
separate,  and  this  has  been  explanation.  For  you  have  seen  the 
intermediate  hidden  phenomena."  But,  I  reply,  I  have  seen 
an  enormous  number  of  other  details,  and,  if  I  fail  to  make  the 
right  connection,  I  have  not  perceived  the  cause.  This  connec- 
tion is  moreover  a  preparation  of  mine,  which  isolates  one  thread 
from  the  tangled  whole.  Is  it  really  not  possible  to  have,  as  we 
say,  the  cause  before  our  eyes,  and  then  fail  to  perceive  it } 
Is  presence  of  a  mass  of  detail  in  perception,  and  apprehension 
of  the  relation  between  two  elements,  exactly  the  same  thing } 
If  one  is  left  at  the  end  of  one's  devoted  labour  incapable  of 
making  such  a  simple  distinction,  I  almost  think  it  would  be 
better  not  to  talk  of  having  "  toiled  through  modern  German 
philosophy  "  {ibid.  p.  80). 

Presentation  to  sense  of  intermediate  detail  is  in  itself  no 
explanation  ;  and  without  an  intermediate  you  may  still 
explain.  If  the  case  is  taken  as  the  instance  of  a  rule,  even 
that  by  itself  is  some  explanation.  I  know  it  has  been  said, 
and  by  those  whom  I  respect,  that  we  have  nothing  here  but 
bare  tautology  ;  that  it  is  frivolous  to  tell  me  that  this  bottle 
\ix^-dks,  because  all  bottles  break.  But  I  confess  I  never  could 
see  the  bare  tautology.  For  the  particular  nature  of  our  one 
bottle  is  in  this  way  connected  with  a  general  law.  It  does 
not  break  because  it  is  a  black  bottle,  or  a  quart  bottle,  or  a 
bottle  made  by  an  infidel  and  on  a  Sunday,  but  because  it 
possesses  an  unstated  quality  common  to  other  bottles.  And 
this  quality  is  a  reason  why  it  breaks.  The  explanation  of 
course  does  not  satisfy  our  desires,  since  we  want  to  make  the 
quality  explicit  ;  but,  so  far  as  it  goes,  it  does  give  us  some 
principle,  and  it  can  not  fairly  be  condemned  as  tautologous. 
In  just  the  same  way  an  apple  falls  down  because  of  gravita- 
tion, and  this  knowledge  connects  the  other  qualities  of  this 
falling  body  with  a  general  attribute  of  material  things.  The 
explanation,  I  admit,  leaves  much  to  be  explained ;  but  I  can 
not  see  that  it  gives  us  mere  words.  On  the  other  hand, 
however,  I  do  not  perceive  that  it  presents  us  with  any 
intermediate  details. 


492  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  II. 

§  9.  But  what  is  the  truth  which  underlies  this  error 
which  we  have  been  considering  ?  It  is  the  mediate 
character  of  all  explanation.  You  show  that  a  connection, 
which  seemed  immediate,  is  not  what  it  seemed.  You  point 
out  the  link  which  serves  to  unite  the  second  element  with 
the  first.  And,  starting  with  this  truth,  the  mistake  we  are 
discussing  goes  on  to  turn  the  link  into  one  constituent  part 
of  the  chain  of  events.  It  .confuses  that  which  is  mediate 
ideally  with  that  which  is  separate  by  an  interval  of  time. 
Thus,  if  Protestants  commit  suicide  more  often  than  Catholics, 
we  explain  this  fact  by  showing  that  suicide  is  increased 
by  civilization,  and  that  in  the  main  Catholics  are  more 
ignorant  and  uncivilized.  Higher  culture  is  mediate  between. 
Protestantism  and  suicide,  but  it  surely  is  not  a  detail  which 
always  intervenes  in  time. 

No  doubt  in  a  very  large  number  of  cases,  in  order  to 
find  the  true  immediate  connection,  you  are  forced  to  enlarge 
the  presented  phenomena.  Where  analysis  fails,  you  supple- 
ment the  given  by  ideal  synthesis,  and  find  in  that  supplement 
the  true  connection.  But  this  is  accidental,  and  it  is  not 
essential.  The  essence  of  the  explanation  of  phenomena 
consists  in  getting  the  relations  pure,  and  by  analysis  of  the 
facts  connecting  their  detail  with  those  pure  relations.  It 
does  not  consist,  and  it  could  not  consist,  in  the  mere 
unintelligent  gaze  through  a  microscope. 

§  10.  It  is  not  my  object  to  ask  in  the  end  what  it  is 
to  explain,  or  to  discuss  the  ultimate  metaphysical  nature 
of  a  law  or  principle  (Book  I.  p.  88).  But  our  rational 
instinct  prompts  us  to  assume  that  we  explain  by  offering 
something  universal  and  something  real.  Now  the  "  laws  "  of 
phenomena  are  assuredly  universal  ;  they  give  not  the  facts 
but  a  garbled  extract.  And  their  truth  is  hypothetical  ;  they 
do  not  even  pretend  that  the  elements,  which  they  connect,  have 
actual  existence.  Hence  the  unfortunate  holder  to.  sensuous 
reality  is  driven  to  face  a  desperate  alternative.  He  must  ex- 
plain the  real  by  what  is  not  real,  or  he  must  assert  that  reason- 
ing and  all  explanation  never  go  beyond  mere  sense-present- 
ment. He  must  persist  that  it  makes  a  mere  addition  to  the 
detail  which  comes  to  the  senses  or  the  sensuous  fancy. 


Chap.  H.]  THE   CAUSE   AND   THE   BECAUSE.  493 

But  we  have  seen  that  his  alternative  is  a  common-place 
blunder.  For  causation,  as  we  know  it,  is  never  the  sequence 
of  actual  phenomena,  or  of  anything  that  could  exist  in  the 
phenomenal  series.  No  imaginary  detail,  added  to  the  given, 
could  do  more  than  increase  the  existing  confusion.  If  the 
history  of  a  thing  is  ever  its  explanation,  this  is  true  because 
history  can  never  be  sensuous.  By  design,  or  even  against 
its  design,  it  must  mutilate  the  facts,  and  substitute  for  them 
a  thread  of  connection  which  never  could  have  been  visible. 
Our  reasoning  and  our  knowledge  of  causal  sequence  is  not 
ideal  in  the  sense  of  an  imaginative  resurrection,  or  a 
miraculous  increase  of  the  sensuous  supply.  It  is  ideal 
because  it  is  intellectual,  because  it  demonstrates  a  connec- 
tion between  universal  elements,  because  it  substitutes  for 
fact,  and  connects  the  facts  by,  a  rational  construction. 

§  II.  Even  where  we  explain  by  assigning  the  cause,  we 
must  rise  into  the  world  of  ideal  arrangement.  For  inference 
is  never  a  mere  presentation,  and  the  knowledge  of  causation, 
we  have  seen,  must  be  reasoning.  The  first  of  those 
questions,  which  we  raised  at  the  beginning  (§  3),  has  been 
answered  affirmatively.  To  know  the  cause  is  to  know  the 
because.  But  the  second  enquiry  remains  unanswered. 
When  we  know  the  because,  or  the  reason  why,  have  we 
learnt  the  cause  ?  Are  both  one  and  the  same  }  We  must 
now  endeavour  to  find  an  answer  to  this  question. 

(ij)  If  cause  were  understood  in  the  sense  of  prhmp/e,. 
then  every  reasoning  would  rest  upon  causation.  It  would 
be  a  cause  in  each  argument  by  virtue  of  which  we  pro- 
ceeded to  get  the  result  from  the  premises.  But  this  identity 
of  principle  and  causal  law  is  the  very  point  which  is 
under  discussion.  And  if  causation  is  confined  to  sequence  in 
time,  the  way  to  put  the  question  is  this.  Can  the  principles 
of  reasoning  be  all  exhibited  as  laws  of  sequences  ?  Must 
the  principle  of  knowledge  be  a  principle  of  becoming  > 

Is  the  because  in  reasoning  always  a  cause  ?  Most  clearly 
we  can  not  make  any  such  statement.  When,  from  A  =  B 
and  B  =  C,  we  conclude  to  the  equality  of  A  and  C,  it  is  hard 
to  see  how  any  common  relation  of  both  with  B  is  the  cause 


494  THE    PRINCIPLES   OF    LOGIC.         [Bk.  IIL  Pt.  II. 

why  A  comes  to  be  equal  to  B.  And  the  enquiry,  once  opened, 
lets  in  a  torrent  of  kindred  objections.  Is  the  proof  in 
geometry  the  cause  of  the  conclusion  ?  Does  the  result  turn 
true  because  of  my  construction,  or  does  it  only  turn  ottt  true 
for  my  knowing  mind  ?  Two  coins  are  proved  to  have 
similar  inscriptions,  because  they  each  are  like  to  a  third,  but 
the  cause  is  not  found  in  this  interrelation.  The  cause  is  the 
origin  from  a  common  die.  If  a  vessel  has  sailed  for  London 
or  Liverpool,  and  we  know  that  it  has  not  sailed  for  the 
former,  we  argue  that  its  course  is  shaped  for  the  latter.  But 
is  our  middle  a  process  of  actual  causation  }  We  can  hardly 
say  this,  and  we  could  give  no  reply  to  an  endless  variety  of 
similar  questions.  So  far  is  the  middle  from  always  present- 
ing us  with  the  cause  of  the  conclusion,  that,  given  an  in- 
ference, we  can  draw  no  presumption  in  favour  of  that  view. 
The  truth  is  in  general  perhaps  more  likely  to  lie  with  the 
other  alternative. 

§  12.  The  question  "Why"  is  always  ambiguous.  It  asks 
indifferently  for  the  cause  of  the  thing,  or  for  the  ground  of 
my  knowledge.  And  the  answer  "  because "  repeats  these 
two  senses.  It  gives  us  alike  the  reason  of  the  fact  and  the 
reason  which  has  led  me  to  believe  in  its  existence.  And  it 
offers  no  sign  by  which  we  may  distinguish  these  radical 
differences. 

The  presumption,  if  there  is  one,  is  against  the  identity  of 
the  cause  and  the  reason.  We  can  not  in  any  case  treat  them 
as  one,  if  we  have  not  some  special  ground  for  our  assumption. 
Wherever  the  premises  represent  a  reality  in  time,  which, 
actually  and  by  its  own  necessity,  goes  into  a  construction — 
wherever  that  construction  itself  is  real,  and  the  quality  or  rela- 
tion, that  appears  in  the  conclusion,  is  its  immediate  result — in 
these  cases,  and  in  these  cases  alone,  the  because  and  the  cause 
must  be  identical.  Wherever,  on  the  other  hand,  a  division  or 
a  junction  is  made  by  the  arbitrary  choice  of  our  minds,  there 
the  reason  for  knowing  and  the  reason  for  being  fall  hopelessly 
asunder. 

§  1 3.  We  shall  return  to  this  theme  in  a  following  chapter ; 
but  for  the  present  we  may  endeavour  to  close  some  sources 
of  dangerous  fallacy.     And  the  first  of  these  rises  from  an 


Chap.  II.]  THE   CAUSE   AND   THE   BECAUSE.  495 

obstinate  confusion.  Every  conclusion  possesses  two  cha- 
racters (p.  2 1 1).  It  is  a  psychical  event  and  a  logical  judgment, 
and  what  is  true  of  it  in  one  of  these  aspects,  may  be  wholly 
false  if  you  take  it  in  the  other.  Now,  if  you  consider  the 
judgment  as  a  mental  occurrence,  the  premises  are  always  part 
of  its  cause.  The  presence  of  these  elements,  together  with  a 
mind  in  a  certain  state,  at  once  sets  up  that  psychical  change 
which  gives  the  conclusion.  The  logical  grounds  are  psycho- 
logical conditions,  and  as  such  they  do  work  in  bringing  about 
the  existence  of  the  result.  But  we  turn  this  truth  into 
absolute  error,  if  we  go  on  to  say  that  the  premises  are  the 
cause,  or  even  part  cause,  of  the  existence  of  that  which  the 
conclusion  affirms.  For  it  is  not  the  content  of  the  final 
judgment  which  thus  has  issued  from  the  synthesis  of  my 
mind  with  the  premises.  It  is  not  the  relation  of  A  to  C 
which  is  caused  by  the  apprehension  of  AB  together  with  BC. 
What  is  caused  is  nothing  but  an  act  of  judgment,  and  that 
act  is  a  genuine  psychical  result,  though  the  content  it  affirms 
may  have  no  kind  of  reality.  It  is  the  bare  event  of  assertion, 
and  not  the  truth  of  the  matter  asserted,  which  follows  as 
effect  from  the  psychical  conditions.  The  cause  in  psychology 
and  the  ground  in  logic  must  be  carefully  distinguished.  The 
two  series  may  run  parallel,  and  may  partly  coincide,  but 
they  are  never  identical. 

§  14.  We  may  notice  in  passing  a  possible  objection  to 
this  coincidence  of  causes  and  grounds.  It  might  be  said  that 
a  cause  must  produce  its  effect,  while  logical  grounds  may  be 
idle  in  the  mind,  and  fail  to  produce  a  logical  result.  But  the 
objection  would  rest  on  a  misunderstanding.  If  we  consider 
the  logical  process  from  its  aspect  of  a  psychical  movement, 
then  no  doubt  we  may  say  that  the  consequence  does  not 
follow  from  the  premises,  unless  another  condition  is  pre- 
supposed. We  have  to  assume  a  mind,  not  merely  present 
but  specially  active,  and  therefore  intervening.  But,  we  may 
urge  in  reply,  that  the  conclusion  can  still  be  said  to  follow, 
since  the  function  exerted  by  the  mind  is  regular.  When  we 
say  "  it  follows,"  we  mean  that  it  follows  given  the  activity  of 
a  normal  intellect,  which  abstains  from  exercising  arbitrary 
choice.     And  our  assertion  is  thus  elliptical  but  is  not  really 


496  THE   PRINCIPLES   OF   LOGIC.         [Bk.  III.  Pt.  XL 

incorrect.  For  this  same  elliptical  character,  we  may  add,  is 
found  in  our  judgments  as  to  cause  and  effect.  We  never 
exhaust  the  whole  mass  of  conditions  which  produce  the 
effect.  The  event  never  comes,  and  it  never  could  come,  from 
the  abstract  selection  which  we  call  the  cause.  We  imply 
the  presence  of  unspecified  conditions,  but  since  these  are 
normal,  we  omit  to  mention  them.  Our  full  statement  would 
run.  Given  such  conditions  in  relation  to  the  real,  and  not  counter- 
acted, and  we  have  the  effect.  In  just  the  same  way,  Given 
certain  premises  in  relation  to  a  mind,  not  blinded  or  biassed, 
and  you  have  the  conclusion.  And  this  answer  may  for  the 
present  be  taken  as  sufficient.  Logical  grounds  may  be 
considered  as  psychical  causes,  as  long  as  you  keep  out  one 
supposition.  But,  if  you  suppose  the  intellect  of  its  own  free 
choice  to  superadd  a  foreign  and  irregular  factor  to  the  premises 
before  it,  then  the  premises  cease  to  cause  the  psychical  con- 
clusion. It  was  this  grave  suspicion  which  underlay  and  gave 
its  strength  to  the  objection  ;  and  it  will  rise  again  to  give 
us  other  trouble  in  the  following  chapters. 

§  15.  And  finally  we  may  point  to  an  obvious  mistake. 
You  may  suppose  that  the  consequent  is  more  concrete  than 
the  ground,  or  the  effect  more  complex  than  the  cause  which 
produces  it.  These  are  parallel  delusions.  If  you  under- 
stand by  "  conclusion  "  the  whole  construction,  this  is  certainly 
more  complex  than  each  of  the  elements,  since  it  is  the  union 
of  these  separate  elements.  But  if  "  conclusion  "  stands  for 
one  part  of  the  construction,  then  not  only  is  the  synthesis  of 
the  premises  more  concrete  than  the  consequent,  but  the  pre- 
mises, if  taken  each  by  itself,  may  none  be  more  abstract. 
So  with  cause  and  effect.  The  effect,  if  you  take  it  without 
isolation,  has  endless  connections  with  other  phenomena,  and 
may  be  said  to  influence  all  succeeding  history.  But  then,  on 
the  othe'r  hand,  why  should  you  choose  tiD  isolate  the  cause  ? 
That  also  exists  by  virtue  of  relation  to  the  existing  universe, 
and  is  just  as  complex  as  you  please  to  take  it.  If  you  were 
to  isolate  effects  and  not  to  isolate  causes,  you  might  emulate 
an  achievement   of  Mr.  Spencer,*  by  a  proof  a  priori  that 

*  See  his  Essay  on  Progress.  The  remark  in  the  text  is  a  criticism 
of  the  proof  as  it  appears  in  that  Essay. 


Chap.  II.]  THE   CAUSE   AND   THE   BECAUSE.  49/ 

history  must  needs  begin  with  the  complex  and  advance 
towards  the  homogeneous.  The  one  demonstration  would, 
logically  speaking,  be  as  valid  as  the  other. 

§  1 6.  Let  us  return  from  our  digressions,  and  gather  the 
result  obtained  in  this  chapter.  We  have  seen  that,  in  order 
to  perceive  causation,  you  must  always  use  reasoning.  The 
cause,  as  we  know  it,  must  be  the  because.  But  there  we  are 
stopped.  We  can  not  assume  that  the  reason,  where  we  have 
one,  is  the  cause  of  the  consequence.  In  some  cases,  no 
doubt,  it  does  appear  as  the  cause,  but  in  others  we  can  not 
see  how  this  is  possible.  And  we  concluded  that  no  general 
presumption  cpuld  be  raised.  But  one  thing  we  could  see  by 
anticipation ;  wherever  the  mind  makes  an  arbitrary  choice, 
wherever  it  seems  to  operate  at  will  (as  in  distinction,  com- 
parison, and  again  in  abstraction),  that  capricious  operation 
can  hardly  represent  the  course  of  events.  And  a  dire 
suspicion  was  then  whispered  within  us.  If  in  inference  the 
conclusion  is  made  what  it  is  by  an  arbitrary  act,  how  can  any 
such  process  be  true  of  reality  }  Our  knowledge  of  the  cause 
will  itself  be  dragged  down  in  the  common  ruin  of  all  our 
reasoning,  and  in  the  end  we  must  doubt  if  there  is  such  a 
thing  as  a  valid  inference. 


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49^  THE    PRINCIPLES   OF   LOGIC.         [Bk.  TIL  Pt.  II. 


CHAPTER  III. 

THE  VALIDITY   OF   INFERENCE. 

§  I.  The  title  of  our  chapter,  welcome  though  it  be,  excites 
foreboding.  We  are  glad  when  we  see  the  harbour  so  near, 
but  the  approach  brings  with  it  an  ultimate  risk  and  a  final 
anxiety.  We  have  escaped  some  perils,  but  our  safety  has 
perhaps  been  dearly  purchased.  In  the  course,  which  we  have 
taken,  the  worst  lies  at  the  end,  and  that  end  is  before  us.  We 
shall  hardly  sail  in  with  vessel  unscathed,  and  with  colours 
flying ;  and,  did  fortune  consent,  we  would  gladly  compromise. 
We  would  change  all  hope  of  a  triumphant  entry  for  the  trust 
that  our  voyage  might  not  end  at  sea.  We  are  resigned  to 
shipwreck,  if  only  by  any  means  something  may  be  saved. 

The  validity  of  inference  has  two  main  senses.  When  we 
ask  if  a  process  of  reasoning  is  correct,  we  may  have  in  our 
mind  two  different  questions.  We  might  ask  if  in  argument 
we  possess  a  strict  counterpart  of  the  nature  of  things,  if  our 
mental  operation  truly  represents  any  actual  process.  And 
this  would  be  the  first  question.  The  second  would  ignore 
this  correspondence  with  reality.  It  would  content  itself  with 
asking  if  the  premises  do  logically  prove  the  result.  And  this 
latter  enquiry  is  the  theme  we  shall  discuss  in  the  present  chap- 
ter.    The  first  and  the  more  difficult  we  still  keep  to  the  end. 

§  2.  But,  when  we  have  confined  the  question  of  our  reason- 
ing's validity  to  the  formal  consequence  of  conclusion  from  pre- 
mises, we  still  find  ourselves  threatened  by  a  double  meaning. 
Our  enquiry  might  be  limited  to  a  search  for  types,  or  we  might 
consider  as  well  our  practical  necessities.  And  the  answer,  it  is 
possible,  might  vary  with  the  question.  For  conceivably  our 
minds  are  dowered  with  a  form  of  ideal  reasoning,  pure  and  im- 
peccable, while  in  practice  our  arguments  are  tainted  with  vice. 
And  so  to  the  question  Is  reasoning  valid  }  we  should  have  to 


Chap.  III.]  THE   VALIDITY   OF   INFERENCE.  499 

return  a  double  answer.  It  would  be  valid  so  long  as  you  made 
it  to  order  with  conditions  that  never  occur  in  practice  ;  while 
each  actual  inference-  might  be  fatally  unsound.  We  intend  to 
lose  sight  of  this  latter  enquiry.  We  do  not  mean  to  ask  what 
sound  performances  of  reasoning  are  practicable,  but  what  types 
of  argument  are  flawless  in  themselves,  without  regard  to  the 
question  if  any  one,  or  no  one,  can  use  them  in  his  work. 

But,  before  we  enter  on  our  doubtful  search,  a  word  of 
caution  must  be  given  to  the  reader.  He  must  not  look  for 
an  ultimate  solution.  In  the  present  chapter,  and  still  more  in 
the  next,  we  abut  upon  provinces  which  we  dare  not  enter. 
It  is  impossible  to  free  logic  from  doubt  and  difficulty,  until 
metaphysics  first  has  cleared  up  its  own  mysteries.  And  so 
we  must  come  in  the  end  to  issues  which  really  lie  in  the  heart 
of  first  principles,  such  issues  as  we  can  not  pretend  to  deal 
with.  Our  immediate  question  will  therefore  not  find  an  un- 
conditional answer.  Inference,  if  valid,  in  the  end  musj,  be  valid 
on  a  certain  hypothesis.  The  conclusion  will  follow,  given  a 
supposition.  Thus  we  can  hope  for  no  more  than  to  arrive  at 
postulates,  assumptions  whose  truth  we  can  not  here  scrutinize, 
but  on  which  our  intellects  are  forced  to  embark,  if  they  mean 
to  serve  us  in  the  voyage  of  life. 

§  3.  Every  inference,  as  we  saw,  falls  into  three  parts.  We 
have  first  a  datum,  then  comes  an  operation,  and  then  follows 
the  result.  And  our  question  really  asks  how  the  last  of  these 
is  related  to  the  first.  What  is  given  appropriates  the  result 
of  an  experiment ;  and  we  demand  the  title  on  which  it 
proceeds.  We  enquire  how  it  justifies  the  taking  to  itself  of 
this  new  possession. 

For  consider,  we  agreed  that  the  result  must  be  new.  If 
we  had  nothing  fresh  we  should  have  no  inference.  But,  if 
so,  what  was  given  us  has  suffered  a  change  ;  it  is  altered  and 
made  different,  and  made  different,  we  must  admit,  through 
our  mind's  operation.  And  yet  in  the  conclusion  this  most 
ominous  fact  is  quietly  suppressed.  We  unblushingly  assert 
that  the  consequence  follows  ;  but  we  know  that  it  follows 
since  we  know  who  has  dragged  it.  We  protest  that  C  is  the 
property  of  A.  How  else,  when  our  hands  first  stole  it  and 
then  secretly  placed  it  in  his  house  ?     And  the   doubt  that 

2  K  2 


500  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  II. 

now  rises,  and  the  suspicion  that  points  at  us,  all  start  from 
this  ground.  If  it  is  you,  they  murmur,  who  have  made  the 
conclusion,  then  it  can  not  be  true  that  you  also  have /b^/;?^  it. 
The  new  attribute  does  not  truly  belong  to  the  subject,  if  your 
choice  and  caprice  is  the  bond  of  their  union. 

We  must  begin  with  a  frank  and  ready  admission.  If  we 
really  did  make  of  our  own  free  will  the  conclusion  which  we 
come  to,  if  the  result  did  not  "  follow  "  of  itself  from  the  datuniy 
but  were  pushed  and  thrust  on  by  our  arbitrary  force  ;  if  (to 
use  a  perhaps  still  more  grateful  metaphor)  we  did  not  "  draw  " 
the  consequence  from  the  bowels  of  the  premises,  but  inserted 
a  product  prepared  by  ourselves — if  we  even  chose  so  to 
influence  our  subject,  that  changed  by  that  influence  it 
modified  its  attributes — then  assuredly  the  process  is  invalid 
and  vicious.  The  conclusion  in  these  cases  would  not  come 
from  the  premises.  It  would  come  from  the  premises  under  a 
condition,  and  its  truth  would  depend  upon  that  condition. 
Or,  more  properly,  the  premises  would  be  wrongly  laid  down  ; 
for  they  should  have  included  the  action  of  our  minds.  And, 
just  as  failing  one  condition  the  others  are  powerless,  and  in 
no  sense  are  any  a  cause  of  the  effect,  so,  failing  the  element  of 
our  arbitrary  choice,  the  premises  we  assigned  are  no  premises 
at  all.  The  conclusion,  if  it  comes,  is  merely  precarious  ;  it  is 
hypothetical.  It  must  wait  upon  chance,  and  the  result  that 
ensues  is  given  but  not  claimed. 

§  4.  If  this  is  agreed  on,  then  the  question  that  remains 
seems  limited  to  one  issue.  Is  there  reasoning  where  the 
conclusion  really  comes  from  the  unhelped  premises  ?  Is  there 
any  where  the  truth  of  the  consequence  does  not  rest  upon  our  in- 
terference .-*     Let  us  proceed  at  once  to  a  particular  example. 

We  will  begin  with  what  seems  to  be  the  strongest  instance. 
In  a  synthetical  construction  without  elision,  we  appear  to  be 
free  from  arbitrary  choice.  Given  A-B  B  — C,  then,  by 
virtue  of  the  common  identity  B,  we  perceive  A  —  B  —  C  ;  and 
the  conclusion  seems  wholly  inherent  in  the  data. 

But  there  comes  an  objection.  The  process  of  inference 
consists  in  putting  the  premises  together.  Of  themselves 
they  lie  idly  apart  in  the  mind,  and  by  themselves  they  would 
still  remain  asunder.     It  is  surely  your  mind  which  supplies 


Chap.  III.]  THE   VALIDITY  OF   INFERENCE.  50I 

them  with  an  unity,  and  which  gives  them  a  connection 
which  they  never  possessed.  You  are  held  in  this  dilemma. 
If  you  say,  A  —  B  and  B  —  C  are  not  really  apart,  then  you 
falsify  your  premises.  But  if  they  are  apart,  then  one  of 
two  things  ;  they  come  together  of  themselves,  or  you  force 
them.  If  you  force  them,  the  conclusion  is  admitted  to  be 
false.  And  they  do  not  come  together,  since  experience 
shows  that  they  may  continue  separate,  and  since  their  change 
to  union  demands  something  effective  which  falls  outside  their 
discontinuous  state.  But  this  agency  must  lie  in  the  motion 
of  your  mind. 

Our  answer  to  this  charge  may  begin  by  rebutting  a  false 
assumption.  Did  the  premises  change  before  our  eyes  into  the 
consequence,  it  would  not  follow  that  therefore  we  changed 
them.  For  the  premises  are  held  in  relation  to  reality,  and 
reality  itself  might  supply  the  condition  which  moved  them 
into  union.  But,  passing  by  this,  let  us  address  ourselves  to 
meet  the  charge  of  interference.  We  may  fairly  enquire,  "  If 
we  have  interfered,  what  is  it  we  have  done  ?  Have  we  taken 
A  —  B  and  B  —  C  from  the  outside  and  coupled  them  together  } 
But  where  is  the  thong  or  the  chain  that  restrains  them? 
What  glue  or  what  nails  have  been  used  to  fasten  them  }  And, 
if  their  attachment  is  part  of  their  substance,  what  is  it  that  we 
have  done  to  strengthen  it  ? 

Our  objector  might  not  find  an  easy  rejoinder,  and  yet  we 
have  hardly  replied  to  his  difficulty.  For  assuredly  we  did 
something,  and  that  deed  was  the  addition  which  brought  out 
the  consequence.  If  a  change  was  not  made,  then  we  had  an 
illusion  ;  and  if  passively  we  stood  spectators  of  a  process, 
then  once  more  we  were  cheated.  And  we  are  fast  in  the 
dilemma — If  nothing  was  altered,  then  there  was  no  inference  ; 
but  if  we  altered  aught  then  the  inference  is  vicious.  And  we 
admit  that  we  were  active. 

§  5.  We  must  meet  the  dilemma  by  a  saving  distinction. 
We  have  here  nothing  to  do  with  the  real  validity  of  our 
reasoning  process,  but  solely  with  its  soundness  as  a  logical 
transition.  And  hence  at  present  we  need  to  regard  our 
reasoning  as  simply  a  change  in  our  way  of  knowing.  But 
this  breaks  through  the  circle  which  threatened  to  be  fatal ; 


502  THE   PPINCIPLES   OF   LOGIC.         [Bk.  III.  Pt.  II. 

for  it  shows  a  possibility  which  was  overlooked.  If,  by  altering 
myself^  I  so  am  able  to  perceive  a  connection  which  before  was 
not  visible,  then  my  act  conditions,  not  the  consequence  itself, 
but  my  knowledge  of  that  consequence.  It  goes  to  make  the 
consequence  in  my  recognition,  but  stands  wholly  apart  from 
this  truth  which  I  recognize.  Though  the  function  of  con- 
cluding depends  upon  my  intellect,  the  content  concluded 
may  be  wholly  unhelped,  untouched,  and  self-developed. 

And  a  logical  postulate,  to  which  we  alluded,  assures  us 
that  this  possibility  is  fact.  Whether  rightly  or  wrongly,  all 
logic  assumes  that  a  mere  attention,  a  simple  retaining  and 
holding  together  before  the  mind's  eye,  is  not  an  alteration. 
If  the  logical  function  does  not  touch  the  content,  if  it  leaves 
A-B  B-C  untampered  with,  then  no  viewing  them  at  once 
or  one  after  the  other,  nor  any  attention  to  one  of  their  elements, 
makes  the  smallest  difference  to  the  truth  itself  My  vision 
is  affected,  but  the  object  is  left  to  its  own  developement. 

Thus,  in  A-B  B-C,  the  identity  of  B  is  the  bond  of 
construction.  If  I  made  that  identity,  I  should  certainly  in 
that  case  have  manufactured  the  consequence.  And  it  may 
be  contended  that  it  lies  in  my  choice  to  see  or  to  be  blind, 
and  that  hence  my  recognition  does  make  what  it  perceives. 
Against  such  a  contention  I  can  here  attempt  no  further 
answer.  I  must  simply  fall  back  on  the  logical  postulate,  and 
leave  further  discussion  to  metaphysics. 

§  6.  But  another  objection  remains  to  impede  us.  Though 
our  action  is  confined  to  the  knowledge  of  the  truth,  we  are 
summoned  to  justify  the  truth  of  our  knowledge.  For  the 
content,  which  we  know,  becomes  different  in  the  sequel, 
and  it  does  not  appear  how  truth  can  thus  change.  We  may 
say  that  the  premises  perhaps  are  not  true ;  we  may  confine 
our  scrutiny  to  the  soundness  of  the  consequence ;  yet  the 
puzzle  does  not  vanish.  Though  the  premises  are  false  the 
conclusion  may  be  valid ;  but  how  if  the  end  contradict  the 
beginning  t  If  the  premises  are  true,  they  surely  would  not 
•alter  ;  and  if  they  do  alter  their  first  state  must  be  false.  But 
even  then  the  last  state  will  not  square  with  the  commence- 
ment. It  destroys  the  ground  in  which  it  is  rooted,  and, 
removing  its  own  base,  must  abolish  itself 


Chap.  III.]  THE  VALIDITY  OF   INFERENCE.  503 

Shall  we  meet  this  objection  by  embracing  it  wholly  ? 
Shall  we  say  that  our  reasoning  is  a  process  of  correction  ; 
that  we  start  with  an  erroneous  view  of  the  truth,  and  that  the 
consequence  is  a  necessary  emendation,  which  arises  from  the 
error  when  our  reflection  illumines  it  ?  If  so,  the  conclusion  in 
each  valid  inference  contradicts  its  own  premises.  It  is  no 
extraneous  opposite  which  removes  its  contrary,  and  perishes 
itself  in  that  common  ruin.  It  is  the  opposite  which  appears 
in  the  decease  of  its  parent,  and  presupposes  a  contrary  which 
disappears  into  itself.  The  conclusion  abolishes  the  truth  of 
the  premises,  since,  by  internal  change,  they  pass  into  a  product 
which  contradicts  them. 

This  docrine  might  stagger  the  traditional  logic,  but  in 
the  main  it  would  not  seriously  tend  to  disturb  us.  Yet  we 
can  not  wholly  embrace  its  conclusion.  It  is  true  that  all 
inference  is  a  process  of  correction.  It  is  true  that  it  can  not 
ever  leave  its  starting-point  quite  unmodified.  But  it  is  one 
thing  to  say  this,  and  another  thing  to  admit  that  every  valid 
inference  contradicts  its  own  premises.  No  doubt,  if  all 
change  were  itself  contradiction,  and  if  knowledge  is  changed 
in  the  act  of  reasoning,  we  could  not  infer  without  self- 
contradiction.  But  I  venture  both  to  doubt  the  general  principle 
and  to  discern  an  error  in  the  special  application.  I  admit 
that  in  the  premises  the  terms  A  and  C  appear  separate  from 
each  other,  and  that  this  appearance  is  removed  in  the 
conclusion.  But  I  can  not  see  that  the  premises  do  assert  the 
actual  separation  of  A  from  C.  They  fail  to  affirm  their 
interrelation,  but  they  certainly  do  not  go  on  to  deny  it.  Thus 
the  judgment,  "A  and  C  have  no  connection,"  would  be  made 
by  the  transformation  of  a  privative  absence  into  a  positive 
exclusion  (p.  112).  It  would  turn  a  mere  psychical  matter  of 
fact  into  a  logical  judgment  with  respect  to  content.  The 
appearance  of  A-B  without  any  C  is  denied  in  the  conclusion 
which  gives  their  union  ;  but  the  judgment  A-B  was  not  that 
appearance,  nor  is  this  judgment  in  any  way  otherwise  denied. 
It  is  increased  but  not  abolished.  There  is  nothing  abolished 
but  our  own  false  prejudice,  that  what  does  not  appear  as  the 
element  in  a  whole  is  tJierefore  independent, 

§  7.  In  the  example,  which  we   have  taken,  my  arbitrary 


504  THE   PRINCIPLES  OF   LOGIC.         [Bk.  IIL  Pt.  II. 

choice  does  not  influence  the  result.  I  may  choose  to  attend 
or  not  to  attend  ;  I  may  retain  and  consider,  or  pass  by 
bhndly.  And  so  much  as  this  is  left  to  my  caprice.  But 
suppose  that  I  consider,  then  the  premises  themselves  pass 
into  the  result.  In  what  sense  my  mind  co-operates  in  that 
passage,  is  a  question  of  first  principles  which  we  can  not 
discuss.  But  it  is  clear  that  my  private  desire  and  preference 
have  no  part  in  the  issue.  Once  resolved  to  see,  I  am 
powerless  to  alter  the  object  of  vision. 

If  we  come  next  to  those  inferences  which  use  an  elision, 
and  where  the  result  does  not  stand  as  the  whole  A  —  B  —  C, 
but  is  lessened  to  A  —  C,  we  must  speak  with  more  caution. 
The  elimination  of  B  depends  upon  our  choice.  We  must  join 
A  —  B  ^  C,  but  to  strike  out  B  is  by  no  means  compulsory.  If 
so  the  conclusion  will  in  part  be  arbitrary.  Is  it  therefore 
unsound  ? 

It  may  be  unsound.  If  we  ventured  or  forgot  ourselves 
so  far  as  wholly  to  ignore  the  middle,  if  we  stepped  from  the 
construction  to  the  absolute  assertion  of  one  part  of  its 
content,  we  might  make  a  common  and  most  dangerous 
mistake.  If  we  intend  to  set  up  A  —  C  by  itself,  we  must  avow 
the  transition  and  be  ready  to  justify  it  And  tacitly  to 
assume  the  independence  of  A  —  C  is  a  logical  mistake. 

But  elision  does  not  need  to  involve  this  error.  It  should 
mean  no  more  than  the  assertion  of  A  ^  C,  subject  to  conditions 
left  unexpressed.  Since,  A  being  given,  there  follows  a 
construction  in  which  we  are  able  to  perceive  A  —  C,  we  may 
say  that  A--C  is  the  mediate  consequence.  Or  it  follows 
hypothetically  at  once,  if  B  becomes  implicit  and  is  thrown 
into  the  base  which  underlies  the  connection  (cf.  Book  1.  pp. 
88^0).  Our  assertion  is  elliptic,  but  in  this  case  is  not 
vicious.  On  the  other  hand  it  becomes  unsound,  if  we  pass  from 
the  privative,  "  I  perceive  mere  A-C,"  to  the  exclusive  "  I  ca7i 
not  see  anything  else,  and  so  nothing  else  but  A-C  is  real." 

§  8.  We  shall  return  to  this  point  when  we  come  to  discuss 
the  validity  of  abstraction.  But  at  present  we  must  mark  a 
division  in  our  subject.  There  are  certain  reasonings  in  which, 
as  we  see,  we  do  nothing  but  attend  or  consider  logically. 
And  it  is  a  postulate  that  such  perception  docs  not  alter  the 


Chap.  III.]  THE  VALIDITY   OF   INFERENCE.  505 

object.  These  reasonings  may  go  on  to  employ  elimination, 
and  this  addition  is  arbitrary.  But  the  conclusion  is  still  sound 
if  the  addition  is  recognized.  It  becomes  to  that  extent 
hypothetical,  and,  though  elliptic,  it  may  stand  ;  for  it  does 
not  affirm  that  mere  A-C  exists,  but  that  A-C  is  kjtow7t. 

But,  after  escaping  this  first  wave,  we  are  met  by  a  rising 
sea  of  inferences  which  all  seem  arbitrary  from  first  to  last. 
For  I  need  not  compare,  and  I  need  not  distinguish.  Again 
neither  in  Arithmetic  nor  in  Geometry  am  I  compelled  to 
construct  or  forced  to  analyze.  I  now  do  more  than  attend 
to  the  developement  of  the  object.  My  own  hands  have  inter- 
fered, and  have  procured  the  experiment  which  gives  the 
result.  And,  if  so,  the  conclusion  must  surely  be  capricious, 
or  at  least  must  be  laid  down  quite  conditionally. 

Let  us  take  the  instance  of  free  spatial  construction.  If  I 
move  A,  B,  and  C,  and  arrange  them  so  as  to  stand  in  certain 
relations,  I  can  not  proceed  to  predicate  this  result  of  A,  B,  and 
C.  Hurdles  by  themselves  will  not  make  a  sheep-fold,  and 
you  can  not  go  straight  from  the  one  to  the  other.  The 
activity  of  the  shepherd  must  be  added  to  the  grounds,  it  must 
be  supposed  and  then  implied  in  the  consequence.  For  the 
shepherd  himself  does  not  follow  from  the  hurdles,  and  we  can 
not  regard  him  as  a  condition  involved  in  A,  B,  and  C.  Hence 
we  must  transform  our  experiment  either  by  adding  something 
to  the  original  data,  or  by  recognizing  a  condition  when  we 
state  the  result.  Otherwise  that  result  is  palpably  vicious. 
And  the  doubt  may  arise  if  this  fatal  alternative  stops  short 
with  our  instance  of  free  spatial  construction. 

§  9.  It  threatens  to  ruin  in  the  first  place  comparison.  For 
that  is  a  process,  and  the  data  compared  are  surely  quite 
passive.  Can  we  say  that  A  and  B  work  out  their  own 
likeness,  any  more  than  hurdles  work  into  a  sheep-fold  ?  Are 
they  like  ?  Is  it  them  which  I  see  to  be  similar  ?  Is  it  not 
some  product  of  my  work  upon  them,  and  some  capricious  ad- 
dition which  really  owns  the  predicate  ?  And  the  same  with 
distinction.  Does  my  process  but  colour  an  element  which 
already  was  there  in  the  premises,  or  have  I  added  an  agent 
which  by  combination  has  produced  a  new  result  1  If  all  I  know 
is  that  something  not  seen  has,  by  virtue  of  my  act,  become 


506  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  II. 

plainly  visible,  by  what  right  do  I  claim  to  have  simply  made 
visible  and  not  rather  to  have  made  ?  Nor  will  arithmetic 
escape.  For,  as  we  saw  long  ago,  one -and  one  are  not  tw^o  ; 
they  become  the  integer,  and  their  becoming  seems  no  change 
that  arises  in  themselves.  But,  if  so,  they  are  not  the  actual 
subject  which  appropriates  the  sequel :  our  hand  is  responsible 
and  can  not  be  disowned.  And  geometry  follows  to  a  com- 
mon doom.  Do  those  wonderful  constructions  grow  out  of  the 
data,  like  branches  from  a  tree  }  Are  those  necessary  pictures 
mere  sketches  of  the  object  ?  Were  w^e  not  more  right  when 
we  likened  them  to  builder's  scaffolding,  and  should  we  not 
think  here  of  those  diagrams  of  operations,  where  we  see 
depicted  the  hand  and  the  knife  ?  The  processes  of  dis- 
tinction comparison  and  construction,  all  show  logical  pre- 
sumptions where  mistake  is  ruinous,  and  where  nothing 
supports  the  ground  which  we  stand  on. 

§  10.  And  so  once  more  we  have  to  fall  back  upon  a 
postulate.  Metaphysics  alone  can  judge  if  we  are  right,  but 
in  logic  we  are  forced  to  assume  that  some  processes  do  not 
modify  their  consequence.  We  work  round  the  content  and 
do  nothing  upon  it.  Thus  retention  and  joint  'notice  were 
supposed  not  to  influence  the  object  of  vision.  And  here  once 
again  we  assume  that  comparison  and  distinction  and  synthesis 
do  not  touch  nor  alter  the  content  of  the  given,  but  simply 
remove  an  obstacle  to  our  sight,  or  aid  that  sight  by  artificial 
reflection.  It  is  not  with  these  as  it  was  with  our  sheep-fold. 
The  position  of  the  hurdles  made  the  sheep-fold  itself,  and  the 
act  of  the  shepherd  did  alter  that  position.  But  here  it  is 
something  in  the  hurdles  themselves,  their  quality,  or  their 
number,  or  again  their  magnitude,  which  appears  no  doubt 
when  the  sheep  have  been  folded,  but  itself  can  not  have  been 
made  by  the  shepherd.  Apart  from  correction  by  the  study 
of  first  principles,  the  shepherd  must  predicate  the  sequel  of  the 
origin.  He  would  not  be  right,  if  he  inserted  an  intermediate 
condition.  Assuredly,  without  his  capricious  act,  he  might 
never  have  come  to  see  the  conclusion  ;  but,  seen  or  unseen, 
the  conclusion  was  still  there.  The  process  has  but  altered  an 
imperfect  vision ;  his  want  of  perception  has  been  changed  to 
plenty.     It  is  he  that  has  chosen  to  let  in  the  light  ;  but  the 


Chap.  III.]  THE   VALIDITY   OF   INFERENCE.  5^7 

object,  our  logical  postulate  assures  us,  was  there  from  the 
first  and  there  unconditionally.  Where  we  state  the  mere  truth, 
we  are  bound  to  eliminate  the  middle  operation. 

And  our  postulates  give  us  the  same  right  of  confidence, 
when  we  take  an  idea  and  suppose  it  to  be  real,  or  when 
suggestion  of  predicates  brings  out  a  response  on  the  part  of 
the  subject.  In  these  cases  once  more,  though  our  viewing  of 
the  sequel  is  conditioned  by  our  choice  and  our  arbitrary  act, 
yet  the  view,  which  we  perceive,  we  must  take  as  unconditional. 
The  process  once  more  has  not  modified  the  content.  It  has 
placed  it  in  experiment  and  prepared  it  for  observation,  but 
has  left  its  essence  unchanged  and  unbiassed. 

§  II.  It  is  different  when  we  come  to  the  process  of 
abstraction.  Where  we  separate  ideally  one  element  from  the 
whole,  we  not  only  perform  an  operation  on  the  given.  We 
not  only  make  a  leap  from  the  known  to  the  unknown,  when 
we  attribute  to  the  given  the  result  of  the  act,  but  we  also  make 
this  venture  on  our  own  responsibility.  It  is  a  logical  in- 
stinct that  prompts  us  to  the  act ;  but  no  logical  postulate 
guarantees  the  outcome.  Reasoning  by  abstraction  has  a 
fatal  defect. 

For  how  shall  we  tell,  and  what  justifies  our  confidence, 
that  our  element  remains  when  the  rest  is  removed  ?  We  are 
burnt  and  we  go  from  this  to  "  Fire  burns."  We  strike  out 
the  mass  of  accompanying  detail,  and  treat  the  residue  as 
belonging  to  the  real.  But  who  goes  surety  that  the  roots  are 
not  twisted,  that,  in  cutting  between  the  reality  and  its  detail, 
we  have  not  severed  some  fibres  of  the  selected  element  t  If 
we  find  that  a  —  bvs^  true  within  x,  on  what  ground  do  we  rest 
for  our  desperate  leap  to  the  assertion  that  a  —  b\^  true 
without  condition  ?  It  is  one  thing  specially  to  notice  a 
member.  It  is  one  thing  to  say  that  this  member  at  any  rate 
is  certainly  here.  It  is  quite  another  thing  to  take  that 
member  apart,  and  to  assume  that,  by  itself,  it  remains  what 
it  was  when  it  lived  in  the  whole.  This  fatal  confusion 
between  theory  and  fact,  this  blind  assumption  that  our 
intellect's  work  must  always  present  us  with  the  nature  of 
things,  is  a  special  trait  of  the  "  Philosophy  of  Experience." 
Bad  metaphysic  supports  it  against  logic  and  the  cry  of  facts. 


508  THE   PRINCIPLES   OF   LOGIC.         [Bk.  IIL  Pt.  XL 

§  12.  If  we  mean  to  keep  clear  of  a  dangerous  venture 
and  really  to  prove  the  conclusion  which  we  reach,  then, 
unless  by  way  of  an  elliptical  statement,  we  can  not  eliminate 
where  we  fail  to  analyze.  If  you  wish  to  remove  one  part 
from  a  whole,  and  maintain  it  away  from  its  original  context, 
you  must  find  what  elements  constitute  that  whole,  and  you 
must  find  exactly  what  each  contributes.  For  you  can  not 
tell  otherwise  what  it  is  you  are  taking,  and  how  much  is  left. 
Your  cutting  may  not  merely  loose  the  string  of  a  bundle.  It 
may  have  utterly  destroyed  the  connection  which  maintains 
the  parts  in  existence.  And  the  result  of  this  is  that  correct 
abstraction  is  guaranteed  by  nothing  save  actual  experiment. 
In  fact,  or  ideally,  you  must  divide  the  whole  into  certain 
elements,  and  you  then  must  make  trial  with  these  several 
factors.  You  may  find  that  the  whole  falls  asunder  into 
parts,  you  may  find  that  this  whole  can  be  reproduced,  when 
experiment  puts  the  parts  together,  and  that  the  parts  all 
remain  unchanged  in  the  process.  You  may  find  that  with 
any  arrangement  the  parts  maintain  their  character,  and  that 
the  qualities  of  the  arrangements  make  no  difference  to  that 
character.  And  if  you  were  able  finally  to  isolate  a,  you 
then  would  see  if  indeed  the  consequence  were  really  b. 
Wherever  this  process  is  taken  as  possible,  elision  and  abstrac- 
tion will  demonstrate  truths.  But  elsewhere  their  result  is 
precarious  and  doubtful.  It  suffices  to  suggest,  but  it  can  not 
prove. 

§  13.  If  I  begin  to  reason  with  the  integer  four,  I  can 
divide  this  integer  into  separate  units,  and,  by  combining 
these  units,  I  can  once  more  produce  the  quality  of  the  whole, 
while  every  unit  remains  unchanged.  By  a  number  of  specific 
ideal  experiments  I  satisfy  myself  that  the  units  are  indifferent 
to  their  junction  in  this  integer,  and  may  be  freely  treated  as 
independent  elements.  For  example  I  can  show  that,  first 
taking  one  unit  and  then  adding  another,  I  get  the  integer 
two,  and  that  I  am  safe  in  ignoring  and  abstracting  wholly 
from  the  totality  four.  All  this  is  quite  obvious,  and  the 
important  point  is  that  my  abstraction  rests  on  specific 
experiment.  I  neglect  the  given  whole  and  eliminate  its 
detail,  because,  within  my  actual  experience,  I  have  destroyed 


Chap.  III.]  THE   VALIDITY  OF   INFERENCE.  509 

that  whole,  and  have  seen  that  the  residue  will  stand  without 
it.  If  I  take  two  from  four,  I  know  that  two  is  left,  since  I 
have  proved  that  the  integer  does  not  inter-connect  the  units 
in  such  a  way  as  to  qualify  them.  But,  failing  this  experi- 
ment, my  abstraction  might  be  vicious.  In  removing  one 
half  of  the  integer  four,  I  might  have  sapped  and  ruined  the 
other  half 

This  is  not  the  place,  nor  am  I  sure  that  it  belongs  to 
logic,  to  discuss  the  limits  of  demonstrative  proof  in  the 
sciences.  What  logic  may  hold  fast  is  the  assurance  that, 
without  a  priori  experiment,  arithmetic  could  not  start.  And 
it  is  certain  that  soon  we  arrive  at  provinces  where  such 
experiment  is  impossible.  In  dividing  the  wholes,  if  we  could 
divide  them,  we  should  modify  the  parts  ;  and  in  summing 
these  parts  we  should  not  regain  the  wholes.  We  are  here  as 
powerless  to  construct  the  facts  a  priori^  as  we  are  to  dissect 
them  by  ideal  analysis.  And  when  these  regions  are  reached, 
as  they  very  soon  are  reached,  then  our  logical  abstraction 
becomes  a  venture,  and  its  result  can  never  amount  to  proof 

§  14.  I  must  return  once  more  here  to  a  fashionable  error. 
The  idea  that,  apart  from  specific  experiment  external  or 
ideal,  you  can  start  with  the  individual  and  go  on  to  prove 
an  abstract  universal,  is  wholly  erroneous.  The  so-called 
"  Method  of  Difference  "  involves  a  downright  logical  mistake. 
It  is  subtraction  employed  where  arithmetic  is  not  known  to 
be  even  possible  (cf  Book  11.  p.  339). 

From  the  given  total  K^  —  df,  by  removal  of  B— /,  we 
abstract  K  —  d,  and  we  argue  that  A  — ^  is  true  of  reality. 
But  our  reasoning  depends  on  the  unwarranted  assumption 
that  in  AB  —  df,  we  have  nothing  but  units.  Take  the  simple 
example,  "2 -{-4—1  makes  the  integer  five,  and  two  units 
apart  from  that  whole  integer  are  two,  therefore  4  -  i  has 
the  quality  of  five,  or  is  at  least  a  part  of  the  cause  of  that 
quality."  This  strict  application  of  the  boasted  method, 
unless  yott  confine  its  result  to  the  individual  ijtstance,  brings 
forth  what  to  me  appears  an  absurdity.  And  the  reason  is 
obvious.  The  Method  identifies,  in  the  whole  and  outside  it, 
both  B  and  /.  And,  standing  upon  the  Identity  of  Indiscern- 
ibles,  it  is  so  far  right.     But  then  it  goes  on  to  assume  the 


5IO  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  II. 

absence  of  difference.  It  takes  for  granted  that  A  and  B 
make  no  difference  to  each  other.  It  takes  for  granted  that 
df  is  nothing  beyond  a  mere  sum.  It  assumes  that  the 
threads,  from  AB  to  df,  neither  cross  nor  are  twisted,  but  run 
side  by  side.  And  this  enormous  presumption  has  no  sound 
base.  It  could  be  justified  by  nothing  but  a  specific  experi- 
ment, ideal  or  external,  which  would  show  that  KQ  —  df  is 
this  bare  addition  of  units.  Without  this  it  is  precarious, 
most  useful  as  a  tentative  means  of  enquiry,  but  unsound  and 
imposturous  if  you  take  it  as  proof.  We  feel  tempted  to 
re-christen  the  Method  of  Difference  as  "  the  method  which 
shuts  its  eyes  to  differences." 

§  1 5.  Probability  is  increased  with  the  number  of  examples. 
If  to  "AB-^/,  B-/"you  go  on  to  add  "AC-^^,  C-^," 
"AE  — <^/^,  E  — /^,"  and  "AF  —  di,  F  —  i,"  you  approximate 
towards  the  certainty  of  A  —  d.  But  you  never  can  demon- 
strate ;  you  never  can  show  that  d  follows  from  A  wit/i  any 
condition,  and  still  less  that,  if  A  were  given  by  itself  and  uncon- 
ditioned, the  result  would  be  d.  For  you  can  not  presume 
that,  apart  from  correlatives,  A  could  even  exist. 

And  I  venture,  in  this  connection,  to  raise  a  doubt  which 
deeply  affects  some  views  of  first  principles.  We  are  some- 
times asked,  in  accents  of  wonder,  how  we  come  to  believe 
that  Reality  is  one.  That  enquiry  is  quite  reasonable,  but  in 
my  turn  I  sometimes  feel  inclined  to  wonder  what  possible 
ground  could  assure  us  of  the  opposite.  For  not  all  of  us 
follow  the  "  School  of  Experience  ; "  we  are  not  all  equipped 
with  an  a  priori  principle,  which  tells  us  that  to  every 
distinction  of  the  mind  a  division  corresponds  in  the  actual 
world.  We  some  of  us^  still  like  to  start  with  facts,  and  still 
keep  up  some  prejudice  for  regarding  them.  And,  if  so,  it  is 
difficult  to  see  what  argument  from  fact  could  secure  our 
conclusion.  For  in  actual  experience  we  never  can  find  a 
thing  by  itself ;  it  is  obvious  that  some  context  will  always  be 
present  there.  And  if,  with  indefinite  variations,  the  thing 
remained  visible  in  all  our  contexts,  that  could  hardly  prove 
that  without  any  context  the  thing  would  exist.  If  we 
showed  that  our  changes  all  made  no  special  difference  to  the 
element,   would    that    tell    us    that   everything   contributed 


Chap.  III.]  THE   VALIDITY  OF   INFERENCE.  5 1 1 

nothing  whatever  and  at  all  ?  And  the  doubt  that  arises  is, 
whether  our  conclusion  does  not  rest  on  the  vicious  abstrac- 
tion we  have  noticed  ;  whether,  in  short,  supposing  that 
single  elements  were  real  by  themselves,  it  would  be  possible 
to  get  to  know  this  truth  by  anything  else  than  an  unsound 
reasoning. 

We  saw,  indeed,  that  analysis  and  abstraction  were  often 
legitimate.  But  then  consider  the  difference  of  the  cases. 
Quite  apart  from  the  fact  that  arithmetic  deals  with  unreal 
abstractions,  what  is  it  that  is  shown  with  respect  to  the  units  ? 
Is  it  proved,  or  can  it  be  proved,  that  units  are  independent 
of  every  integer  t  Did  we  not,  on  the  contrary,  merely  show 
their  complete  indifference  to  any  particular  integer  ?  But  it 
is  one  thing  to  be  free  from  this  or  that  complex,  and  another 
thing  to  stand  entirely  absolute.  And,  if  we  tried  to  show- 
that  an  unit  could  possibly  exist  by  itself,  we  should  pass 
from  arithmetic  to  bad  metaphysics.  For  the  isolation 
implies  an  ideal  integer,  an  invisible  whole ;  and  it  implies 
definition  by  relation  to  other  excluded  units.  If  we  recog- 
nize these  elements  our  unit  is  not  solitary  ;  if  we  ignore 
them  we  fall  into  vicious  abstraction. 

Where  analysis  is  possible,  there  always  remains  an  implicit 
condition.  And  this  rises  as  an  obstacle  whenever  we  attempt 
to  raise  our  result  to  absolute  existence.  But  where  analysis 
and  construction  can  not  be  effected,  there  abstraction  is  always 
a  hazardous  guess,  and  can  never  amount  to  a  logical  proof. 
And  with  this  last  warning  we  may  leave  a  most  dangerous 
source  of  widespread,  insidious,  and  fatal  delusion. 

§  1 6.  We  may  go  on  to  deal  with  other  difficulties.  The 
Disjunctive  argument  consisted,  as  we  saw,  in  the  passage  from 
a  single  possible  predicate  to  its  assertion  as  actual  (p.  385).  This 
transition  depends  on  a  logical  postulate,  and  I  do  not  propose 
to  discuss  it  farther.  It  would  be  easy  to  raise  metaphysical 
objections,  but  they  would  fall  beyond  the  limits  of  this 
volume. 

When  we  have  once  got  to  a  sole  remaining  possibility,  our 
inference  is  then  to  be  taken  as  valid.  But  how  can  we  be 
sure  that  we  ever  have  reached  this  ground  of  inference  ?  We 
saw  that,  in  the  end,  disjunction  depended  upon  our  impotence 


512  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  IL 

to  find  any  other  predicate.  It  seemed  to  rest  on  the  experi- 
ment, "  I  can  not  otherwise  and  therefoj^e  I  must."  And  this 
process  calls  up  the  gravest  suspicion.  To  state  and  settle 
the  doubts,  which  it  gives  rise  to,  would  imply  the  discus- 
sion of  some  subtle  questions  that  would  lead  us  too 
far  into  metaphysics.  Omitting  these,*  we  must  content 
ourselves  with  trying  to  consider  the  problem  from  its  logical 
side. 

§  17.  In  disjunctive  .reasoning  we  have  a  subject  A.  This 
subject  possesses  a  quality  x,  and  x  is  determined  as  one  of 
the  discrepants  a,  b,  and  c.  We  go  from  the  denial  of  a  and  b 
to  the  assertion  of  c;  and  this  process  assumes  that  x  is 
exhausted  by  a^  b,  and  c,  and  that  any  other  predicate  will  fall, 
not  outside,  but  within  these  areas.  But  how  do  we  know 
that  X  is  exhausted  }  How  can  we  tell  that  no  other  predicate, 
such  as  d,  is  possible  .?  Our  inference  is  ruined  unless  this 
condition  is  fully  satisfied. 

Now  in  subordinate  reasonings,  where  we  start  from  and 
rest  upon  preconceptions,  it  is  easy  to  have  a  complete 
division.  The  division  is  complete  because  we  have  taken 
certain  things  for  granted.  But  this  postulated  omniscience, 
this  factitious  totality,  must  come  to  an  end.  When  we  reach 
those  assumptions  from  which  we  proceed,  we  have  then 
to  face  the  general  problem.  How  can  we  ever  exhaust  possi- 
bilities, and  how  can  we  know  that  they  ever  are  exhausted } 

Suppose  that,  in  the  end,  we  are  forced  to  avow  that 
we  rest  upon  impotence,  that  we  are  unable  to  find  any 
other  suggestion,  and  that  certainly  nothing  else  will  appear. 
Is  not  this  the  admission  that  we  stand  on  nought  but  a 
privative  judgment.^  And  is  not,  this  foundation  hopelessly 
unsound  ? 

§  18.  There  is  one  way  of  escape.  The  rejection  of  an- 
other and  opposite  predicate  may  perhaps  after  all  not  be 
based  on  privation.  It  may  really  spring  from  exclusion  by 
means  of  a  positive  attribute.  For  suppose  that  our  subject 
has   the   quality   c,   and   that   this   quality   is    unseen.     The 

*  In  my  notes  for  this  chapter  I  went  somewhat  more  fully  into  this 
question,  but  found  I  should  occupy  too  much  space  with  questions  I 
was  not  sure  were  logical. 


Chap.  III.]  THE  VALIDITY  OF   INFERENCE.  $13 

experiment  by  disjunction  might  succeed  in  making  us 
apprehend  c.  It  might  cause  what  is  latent  to  turn  explicit, 
while  the  real  ground  we  possess  for  the  existence  of  c  might 
not  lie  at  all  in  the  process  of  exhaustion. 

To  explain — when  a  and  b  are  rejected,  the  base  of  rejec- 
tion may  not  be  any  defect  in  A,  but  rather  the  presence 
of  c  which  operates  although  unseen.  And  this  principle 
goes  further.  When  we  ask,  Is  there  anything  possible  but  ^, 
it  may  be  once  again  the  presence  of.^  which  excludes  the 
idea  of  an  opposite  alternative.  But,  if  so,  our  conclusion 
would  be  fully  guaranteed.  We  are  assured  that  nothing  but  c 
is  possible,  since  the  attempt  to  find  a  disparate  suggestion 
has  made  c  explicit.  And,  if  c  were  not  real,  we  should 
find  ourselves  left  with  a  conditional  judgment,  in  which  the 
predicate  would  deny  the  subject.  But  the  consequence  is 
that  our  impotence  is  not  the  real  cause  of  the  conclusion  to  c. 
It  is  c  on  the  other  hand  which  has  caused  our  impotence.  Its 
strength  does  not  lie  in  the  weakness  of  our  minds,  though 
the  experience  of  our  weakness  proves  its  strength.  In  other 
words  our  knowledge  of  its  presence  depends  indeed  on  our 
failure  to  banish  it,  but  its  covert  agency  it  is  which  procures 
our  open  failure.  The  essence  of  our  reasoning  does  not 
really  consist  in  tollendo  ponere.  Ostensibly  tollens  its  exhaus- 
tion and  elision  are  a  useful  show  provocative  of  truth.  From 
a  tacit  position  it  works  tollendo,  to  attain  thereby  an  explicit 
ponere  of  this  latent  quality.  It  is  thus  a  threatened  con- 
tradiction which  compels  our  subject  to  reveal  a  hidden  but 
virtual  pretension. 

It  is  scarcely  worth  while  to  add  an  illustration.  I  may 
deny  that  an  actual  number  can  be  infinite,  not  because  I  am 
unable  to  form  the  idea,  but  because  it  contradicts  a  quality  of 
the  subject  "  actual  number."  I  may  be  sure  that  a  "  Personal 
Devil "  is  nothing,  not  merely  because  of  the  absence  of  reason 
for  belief  in  his  existence,  but  because  he  implies  a  self- 
contradiction.  An  immoral  agent,  who  was  utterly  wicked, 
would  fall  outside  the  sphere  of  morality  ;  for  badness,  like 
goodness,  involves  a  collision,  and  ceases  to  exist  when  you 
make  it  absolute. 

§   19.  Where   this   kind   of  disjunctive   inference   can    be 

2  L 


514  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  IL 

practised,  the  conclusion  it  procures  is  logically  certain.  For 
the  predicate,  which  emerges,  is  not  won  by  exhausting  every 
possible  antagonist.  The  subject  has  not  actually  been 
altered  by  the  choice  of  our  ideal  experiment.  It  remains 
what  it  was.  Our  own  eyes  are  the  real  subject  which  has 
suffered  the  operative  process,  but  nothing  is  removed  save 
impediments  to  vision.  If  we  keep  to  the  limits  already  laid 
down,  then  logic  is  pledged  to  bear  us  unharmed  through  all 
logical  objections. 

We  are  open  to  attack  from  another  quarter  ;  for  we  may 
fairly  be  charged  with  the  sin  of  dese?rtion.  The  process,  which 
we  adopt,  may  be  saved  from  every  assault  of  the  enemy  ; 
but  what,  it  may  be  asked,  has  become  of  the  disjunction? 
For  this  suggestion  of  an  opposite,  which  leads  to  reflection  on 
what  lay  in  our  minds — this  going  from  the  experience  of  "  I 
can  not  otherwise"  by  an  inference  to  the  ground  of  our 
incapacity — (however  sound  and  however  ultimate  the  process 
may  be)  does  not  seem  a  disjunctive  argument  at  all.  Since 
the  residue  is  in  fact  a  preconception,  since  the  exhausted 
alternatives  were  never  possible,  the  conclusion  does  not 
depend  on  exclusion.  It  is  not  in  effect  the  mere  assertion  of 
a  residual  element,  and  this  show  and  pretence  is  a  hollow  form 
which  is  simply  deceptive. 

There  is  truth  in  this  objection.  The  disjunctive  argument, 
if  you  take  it  seriously,  is  not  the  process  we  have  just 
sketched  and  defended.  This  process  does  appear  in  the  form 
of  disjunction.  An  exhaustion  is  the  mode  in  which  we  clothe 
it,  and  the  shape  which  it  bears,  if  you  take  it  as  a  fashion  of 
opening  our  eyes.  But  the  exhaustion  itself  is  not  that  which 
demonstrates.  The  possibilities  banished  were  never  possible. 
And  the  experiment  is  so  far  from  serving  as  a  ground,  that 
the  process  consists  in  its  total  rejection.  But  the  objection 
may  perhaps  find  its  answer  in  a  doubt.  If  disjunctive 
reasoning  is  not  willing  to  take  the  place  which  we  have 
offered  it ;  if  it  aspires  to  be  more  than  a  road  to  vision,  and 
a  way  of  reflection  which  brings  the  actual  ground  into  light,  is 
it  likely  to  maintain  its  claim  to  existence  ?  Is  our  seeming 
desertion  not  a  counsel  to  throw  off  a  character  assumed,  and 
that  leads  to  condemnation  ? 


Chap.  III.]  THE  VALIDITY   OF   INFERENCE.  515 

§  20.  For,  taken  in  the  guise  which  it  prefers  to  wear,  the 
disjunctive  argument  will  not  bear  a  trial.  Apart  from  a 
borrowed  assumption  of  completeness,  the  ground  it  stands  on 
is  wholly  rotten.  If  it  really  goes  from  the  absence  of  a  and  b 
to  the  presence  of  c,  and  if  it  takes  this  step  because  it  has  failed 
to  find  other  possibilities,  then  it  sins  against  a  cardinal  logical 
principle.  It  treats  a  mere  defect  in  its  knowledge  as  equiva- 
lent to  a  positive  quality  in  the  content.  The  fact  that  A,  as 
it  now  appears,  is  wanting  in  d,  is  no  proof  that  A  —  <^  is  a 
false  proposition.  You  can  not  identify  the  subject,  as  it  stands 
under  psychical  conditions,  with  the  subject  as  fully  determined 
by  content.  You  can  not  in  short,  by  any  kind  of  handling, 
make  a  privative  judgment  become  an  exclusion  (cf.  Book  I. 
Chap.  III.). 

If  my  reason,  for  thinking  that  A  —  ^  is  false,  is  simply  my 
failure  to  find  d  in  A,  then  the  subject,  which  I  deal  with,  is 
the  subject  as  qualified  by  my  mental  defects.  It  is  not  the 
mere  content  A  which  excludes,  but  it  is  A  taken  together 
with  that  stage  of  ignorance,  at  which  my  psychical  history  has 
arrived.  But  this  absence  of  knowledge  does  not  logically 
determine  the  content  A.  It  is  an  abstinence  which  reveals  no 
actual  quality  within  the  subject ;  for  there  can  not  be  virtue 
where  temptation  as  yet  has  not  happened  to  assail. 

To  put  the  case  otherwise,  if  d  is  not  impossible,  if  it  is 
simply  unreal  ;  or,  more  strictly  (since  everything  unreal  is 
impossible),  if  d  is  not  impossible  because,  if  it  were,  a  quality 
of  the  logical  content  A  would  be  contradicted — if  d  is  im- 
possible, because  otherwise  our  knowledge  of  A  would  be 
alteredy  and  if  this  is  the  only  reason  we  can  give  for  d's  non- 
existence— then  our  inference  is  precarious,  its  process  is 
unsound,  and  its  conclusion  but  begged.  We  may  be  forced 
to  put  up  with  it,  but  we  must  not  try  to  think  that  logic 
guarantees  it. 

§  21.  We  may  sum  the  matter  so.  If,  in  saying  "  I  must 
because  I  can  not  otherwise,"  we  mean  "  I  must  not  otherwise 
because  I  do  thus,  and  I  know  that  I  do  thus  because  I  can 
not  do  otherwise,"  then  our  inference  may  not  bear  the  name 
of  disjunction,  but  it  is  thoroughly  sound  and  faultless  in 
principle.     But,  if,  on   the   other   hand,    the   essence   of  our 

2  L  2 


5l6  THE   PRINCIPLES  OF   LOGIC.        [Bk.  Ill  Pt.  II. 

argument  is  "  I  must  do  this,  because  I  do  not  perceive  that  I 
do  aught  else,"  then  that  argument  may  not  reach  a  false 
conclusion,  but,  considered  as  a  proof,  it  is  thoroughly  vicious. 
And,  if  this  is  what  we  mean  by  disjunctive  reasoning,  our 
process  in  the  end  is  based  on  a  fallacy. 

And  this  opens  the  door  to  a  sceptical  doubt.  Must  not 
both  these  varieties,  if  we  determine  to  go  back,  resolve 
themselves  into  cases  of  the  second  ?  Does  our  proof  depend 
on  anything  beside  the  ignoring  of  another  discrepant  alter- 
native ?  This  doubt  does  not  cease  with  the  province  of 
disjunction  ;  it  attacks  the  whole  system  of  our  judgments 
and  inferences.  If  all  judgment  in  the  end  becomes  an 
inference,  when  reflection  suggests  an  excluded  predicate,  and 
returns  to  the  subject  from  that  repulsion — if  this,  as  we  saw, 
is  the  ultimate  inference — does  not  every  judgment  in  this 
way  become  a  vicious  inference  ?  For  it  either  is  held  for  no 
reason  except  that  it  has  not  been  questioned,  or,  when 
attempted,  it  succeeds  in  keeping  its  virtue  for  no  other  reason 
than  the  absence  of  suggestions  fit  to  corrupt  it.  And  this 
absence  is  assuredly  the  chance  of  privation.  We  are  forced 
to  admit  a  theoretical  possibility  of  our  knowledge  being 
otherwise,  if  our  ignorance  were  less.  And,  if  so,  with  each 
predicate,  we  can  not  deny  the  possible  existence  of  unknown 
alternatives.  To  dissent  is  to  assume  something  like  omni- 
science, and  to  agree  is  to  vitiate  every  inference. 

§  22.  We  might  reply  that,  even  if  we  did  not  merely 
assume,  but  really  possessed  entire  omniscience,  we  should 
still  by  the  argument  be  compelled  to  doubt  and  to  dis- 
believe. And  this  consequence,  the  legitimate  offspring  of 
scepticism,  shows  features  distressingly  like  credulity.  But  it 
is  better  to  attempt  a  direct  refutation.  The  sceptical  doubt, 
here  as  elsewhere,  will  at  bottom  be  discovered  not  to  be 
sceptical.  It  assumes  a  foundation  on  which  it  stands  to 
batter  down  its  dogmatic  antagonists,  and  that  foundation 
itself  is  always  uncritical  though  covert  dogmatism.  We  can 
see  this  at  once  in  the  present  case.  We  found  (Book  I. 
Chap.  VII.)  that  the  possible  must  rest  on  the  real.  Possi- 
bilities exist  in  hypothetic  judgments,  and  consist  in  the 
assertion  that,  given  some  conditions,  a  subject  would  certainly 


Chap.  III.]  THE  VALIDITY   OF   INFERENCE.  517 

possess  some  attribute.  This  simple  reflection  has  important 
results.  For  if  you  say  that,  with  every  piece  of  our  know- 
ledge, we  are  bound  to  admit  that  it  might  be  otherwise,  you  as- 
sume that  with  every  subject  you  can  frame  a  valid  conditional 
judgment  in  which  it  acquires  a  discrepant  predicate.  Thus, 
given  A  —  d,  you  assume  the  existence  of  a  possible  c;  and 
since  the  pair,  A  and  d,  are  coupled  not  by  virtue  of  any 
special  attraction,  but  solely  because  d  happened  to  be  there 
when  A  was  unoccupied,  hence  the  relation  A  —  <5  is  itself  but 
possible. 

Now  the  answer  is  this,  that,  if  your  conclusion  is  true,  you 
either  have  failed  altogether  to  prove  it,  or  have  proved  it  by 
means  of  a  false  assumption.  For  you  yourself  have  ignored 
a  possibility.  Suppose  that  your  effort,  everywhere  to  find  a 
disparate  suggestion,  were  somewhere  unsuccessful.  Suppose 
that,  attempting  to  make  a  judgment  in  which  the  subject 
developed  a  predicate  inconsistent  with  the  character  already 
possessed,  you  somewhere  found  j^otir  impotence  and  the 
limits  of  your  thought.  If  you  wish  to  be  sceptical,  you  must 
cease  to  ignore  this  fatal  alternative.  For  seeking  a  possible 
quality  c,  incompatible  with  the  present  judgment  A  — <^,  you 
may  end  for  ever  in  a  blank  defect,  or  for  ever  arrive  at  a 
c,  which  seems  to  be  discrepant  with  b,  but  which  falls  on 
scrutiny  within  its  area.  And,  if  this  is  the  case,  then  to 
doubt  A  —  <^  is  presumptuous  dogmatism.  You  can  not  assert 
that  its  opposite  is  possible,  until  you  are  able  mentally  to 
represent  that  opposite. 

To  doubt  where  you  have  but  a  single  idea,  to  balance 
opposites  where  one  opposite  is  lacking,  to  suppose  that  the 
inconceivable  is  true,  would  be  surely  mere  forms  of  one  self- 
delusion.  The  question  at  issue  turns  on  the  fact  of  there 
being  these  opposites.  The  real  existence  of  these  ultimate 
doubts,  the  very  possibility  of  these  possibilities  is  the  point 
where  you  are  met  by  a  flat  denial.  You  can  not  escape  a 
metaphysical  discussion  by  metaphysical  dogmatism  in  the 
garb  of  scepticism.  And,  whichever  way  we  may  decide  this 
question,  we  certainly  can  not  decide  it  ofl'-hand  by  a  simple 
argument  a  priori.  We  must  meet  the  sceptic  by  a  deeper 
scepticism.     His  conclusion,  if  true,  has  been  merely  assumed. 


5l8  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  IL 

Whether  right  or  wrong  in  the  ultimate  result,  his  process  has 
consisted  in  begging  the  question  at  issue  between  himself  and 
those  who  dissent  from  him. 

§  23.  The  actual  question  belongs  to  metaphysics,  and  we 
can  not  attempt  to  consider  it  here.  A  logical  enquiry  must 
remain  content  with  a  simpler  result.  If  the  subject  of 
privation  be  identified  with  the  true  and  real  subject,  then,  on 
that  assumption,  disjunction  is  valid.  The  formal  conse- 
quence of  conclusion  from  premises  is  then  unimpeachable. 
But  the  premise  which  maintains  complete  exhaustion  is 
merely  precarious.  If,  on  the  other  hand,  we  wish  for  a 
process  which  is  free  from  doubt,  then,  while  it  assumes  the 
form  of  disjunction,  it  must  really  proceed  by  exclusive 
assertion.     It  must  argue  from  presence  and  not  from  defect. 

And,  with  this,  the  remarks  which  we  are  able  to  offer, 
may  come  to  an  end  ;  and  we  shall  say  no  more  on  the  formal 
validity  of  our  types  of  inference.  Dialectical  reasoning  has 
not  been  discussed,  but  would  not  present  us  with  new 
conclusions.  Our  main  result  may  be  so  summed  up.  Argu- 
ments, so  far  as  they  amount  to  demonstration,  have  been 
found  to  depend  upon  logical  postulates.  It  is  assumed 
throughout  that  some  operations  do  but  change  our  power 
of  perceiving  the  subject,  and  leave  the  subject  itself  un- 
altered. And  this  holds  even  where  our  wilful  and  arbitrary 
choice  selects  the  process  and  procures  the  result.  The  gain 
which  the  subject  appropriates  in  the  end,  is  here  its  original 
and  rightful  possession  ;  while  the  loss  and  the  struggle  from 
defect  to  growth  is  the  lot  which  falls  to  our  finite  intelligence. 
But  these  postulates  in  the  end  we  left  unexamined. 

§  24.  We  have  still  before  us  a  very  grave  question.  In 
our  final  chapter  we  must  ask  whether  inference  is  really 
valid  ;  if,  that  is,  beside  making  good  the  conclusion,  its 
process  has  a  claim  to  be  true  of  facts.  We  may  here,  and  in 
passing,  allude  very  briefly  to  another  difficulty.  We  saw 
that,  though  our  types  might  all  be  flawless  and  formally 
accurate,  we  might  still  be  quite  unable  to  use  them.  The 
conditions  required  for  a  demonstration  might  never  occur 
in  actual  practice.  Our  types  might  be  ideals,  visible  in 
heaven,  but  too  far  and  too  pure  for  human  attainment. 


Chap.  III.]  THE   VALIDITY   OF   INFERENCE.  519 

We  may  indicate  the  principal  source  of  our  corruption. 
What  we  use  in  logic  is  ideal  content,  and  that  content,  we 
have  seen,  can  have  by  itself  no  mental  existence.  It  must 
always  appear  under  psychical  conditions,  and  hence  comes  a 
continual  tendency  to  error.  If  we  confuse  the  context  with 
the  actual  content,  we  are  sure  to  vitiate  the  whole  logical 
process.  For  since  we  do  not  know  exactly  what  we  have  in 
our  hands,  what  we  actually  use  and  what  we  neglect,  we 
turn  a  judgment,  that  should  be  categorical,  into  a  judgment 
that  depends  on  a  latent  condition.  The  form,  in  which  the 
conclusion  comes  out,  will  depend  on  the  presence  of  impurity 
in  the  agents.  Take  for  instance  A  — B  and  B  — C  as  pre- 
mises, with  a  result  A  —  C.  The  construction  here  depends  on 
the  identity  of  B  in  both  these  premises.  But  suppose  that, 
in  the  second  premise,  C  is  not  really  connected  with  B  ; 
suppose  that  it  really  belongs  to  Bx,  and  that  we  have 
neglected  to  notice  x.  The  relation  with  C  will  then  depend 
upon  the  context,  while  we  have  assigned  it  to  the  bare  and 
simple  content  B.  Thus  a  condition  has  crept  in  and  has 
destroyed  our  reasoning.  And  hence  to  reason  rightly 
demands  a  purity  which  is  based  throughout  on  elimination. 
Since  we  must  have  identity,  and  can  not  but  have  difference, 
we  depend  for  our  success  on  preserving  the  material,  while 
eliding  the  irrelevant  elements  of  our  premises  ;  and  this 
process  is  subjected  to  the  risk  of  error. 

§  25.  We  can  not  any  further  pursue  this  theme,  but  may 
end  our  chapter  with  another  word  against  the  sceptic.  We 
are  bound  to  admit  some  degree  of  probability  in  favour  of 
the  badness  of  any  one  inference  ;  and  the  sceptic  once  more 
may  urge  his  objection.  If  every  argument  \'^  probably  false, 
how  can  any  argument  be  certainly  true  ?  But  the  answer  is 
simple.  Considering  my  reasoning  as  a  number  of  acts,  I 
conclude  that  I  am  fallible  throughout  the  series.  But  this 
chance  is  mere  antecedetit  probability.  It  may  become  un- 
meaning when  the  instance  is  present  and  actually  before  us  ; 
as  unmeaning  as  the  chances  against  a  die  giving  six,  when 
the  actual  throw  has  been  observed.  And,  if  so,  the  pre- 
sumption of  our  fallibility  may  warrant  a  general  feeling  of 
diffidence  ;  but  it  can  not  affect  any  actual  inference  which  has 


520  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  XL 

once  been  seen  to  exhibit  the  type  required  for  demonstration. 
If  in  the  present  instance  you  can  show  me  no  ground  which 
justifies  doubt,  your  mere  general  probability  is  quite  irrele- 
vant* Whether  it  is  true  that  in  every  case  we  have  actual  cause 
for  hesitation,  is  a  question  of  fact  to  be  settled  by  itself  This 
question  of  fact,  which  perhaps  underlay  the  objection,  and 
which  has  appeared  in  the  answer,  can  not  here  be  discussed. 
We  must  concentrate  our  thoughts,  since  we  are  summoned 
to  encounter  our  ultimate  problem. 

*  There  is  a  somewhat  similar  fallacy  in  Mr.  Spencer's  Psychology, 
vol.  ii.  p.  430.  You  can  not  argue  from  the  general  probability,  that  a 
longer  argument  has  more  chances  of  mistake,  direct  to  the  conclusion 
that  a  short  argument  must  be  more  trustworthy  than  a  longer  one.  In 
order  to  do  this,  you  must  assume  besides,  that  arguments  differ  in  nothing 
material  except  their  length. 


(      521       ) 


CHAPTER  IV. 

THE  VALIDITY  OF   INFERENCE   {continued)* 

§  I.  In  the  foregoing  chapter  we  Hmited  the  question  of 
our  reasoning's  vaHdity.  We  discussed  the  possibility  of 
getting  an  inference  which  amounts  to  demonstration.  We 
asked  whether  any  conclusion  does  follow,  when  the  premises 
are  assumed.  To  this  limited  question  we  were  able  to  return 
an  affirmative  reply,  (if  we  admit  certain  postulates,  then  there 
assuredly  are  types  of  necessary  reasoning.  It  may  be  diffi- 
cult to  practise  the  rules  which  they  enjoin,  but  we  may  say 
at  least  that,  given  the  conditions,  the  consequence  nmst  follow. 
And  so  far,  though  relying  on  the  strength  of  postulates,  we 
have  succeeded  in  holding  the  position  which  we  occupied. 

But  we  now  must  await  a  more  dangerous  attack.  Our 
inference  may  be  valid,  if  valid  is  to  bear  the  sense  of 
conclusive ;  the  consequence  may  follow  and  be  true,  if  the 
premises  are  not  false.  But  what  shall  we  answer,  when 
asked  if  our  reasoning  is  true  in  reality,  and  valid  of  fact 
throughout  all  its  process  ?  It  is  not  enough  to  reply  that 
surely  it  comes  out  true  in  the  end.  For  the  outset  and  the 
journey  might  both  lie  in  a  region  of  convenient  falsehood  ; 
and  the  question,  which  is  pushed  and  which  can  no  longer 
be  fenced  with,  directs  itself  to  this  fatal  weakness.  If  truth 
is  the  ideal  counterpart  of  fact,  can  we  say  that  the  process  of 
our  reasoning  is  truth  ?  Can  we  venture  to  assert  that  our 
mental  operations  are  the  same  with  any  actual  process  in 
things  ?  I3  the  intellectual  experiment  the  parallel  of  a 
movement  in  the  real  universe  t  Our  reasoning,  we  know, 
does  answer  to  the  facts,  but  that  is  not  enough.  Can  we  call 
it  the  literal  expression  of  those  facts  }  Is  reflection  the 
double  of  an  outward  change,  that  shows  feature  for  feature 
in  an  answering  element  ?  Or  is  it  an  indirect  process,  which 
*  Cf  Lotze,  Logikj  Buch  III.  Kap.  4. 


522  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  II. 

results  in  a  picture,  but  which,  taken  in  the  middle,  could  not 
be  recognized  ?  We  may  doubt  if  the  end,  when  we  get  it,  is 
a  copy ;  and  we  may  doubt  still  more  if  the  means  is  a 
copying,  or  in  any  sense  a  counterpart.  * 

§  2.  We  can  not  dwell  on  this  question  in  its  ultimate  form. 
We  can  not  decide  if  an  activity,  which  appears  in  our  reason- 
ing, is  one  with  a  force  that  alters  reality.  It  is  not  that  I  think 
the  question  improper,  but  that  in  this  volume  it  could  not  be 
discussed.  For  the  very  existence  of  any  force  or  activity  is 
itself  a  point  which  we  are  not  able  to  assume  ;  and  without 
this  assumption,  the  question  we  have  mentioned  would  of 
course  have  no  meaning. 

But,  if  we  lay  no  stress  on  the  question  of  activity,  and 
confine  ourselves  mainly  to  the  actual  change,  the  problem  in 
hand  may  thus  be  stated.  In  our  reasoning  a  datum  suffers 
alteration  ;  undergoing  a  change  it  appropriates  the  whole,  or 
at  least  some  part  of  the  new  result.  And  does  the  reality 
transform  itself  in  unison  ?  Do  the  facts  themselves  exhibit 
alterations  parallel  with  the  series  that  appears  in  our 
argument }  Is  this  always  the  case,  and  again,  if  not  always, 
is  it  ever  the  case  in  any  possible  argument } 

§  3.  The  result,  we  have  reached,  forbids  us  to  accept  the 
first  of  these  alternatives.  Where  the  middle  of  our  process 
does  not  answer  to  the  cause,  where  it  is  not  the  reason  of  the 
conclusion's  existence,  but  merely  the  ground  which  we  have 
for  belief  in  it,  in  every  such  case  our  mental  experiment  does 
not  even  pretend  to  reproduce  fact.  The  equality  of  A  and 
of  C  to  B  is  our  cause  for  the  judgment  "  C  is  equal  to  A,"  but 
we  can  not  suppose  that  this  change  in  our  knowledge  has  an 
answering  birth  hi  rerum  natura.  The  last  relation  does  not 
spring  from  the  original  pair.  The  result  in  our  minds  is  no 
actual  result,  the  change  in  our  minds  is  no  change  in  things, 
the  mental  experiment,  if  you  compare  it  with  the  fact,  has  no 
existing  counterpart  at  all.  If  the  real  world  is  not  far  other 
than  it  seems,  then  the  course  of  our  ideas,  at  least  in  this  case, 
can  not  possibly  be  true. 

The  conclusion  does  not  really  result  from  the  func- 
tion ;  for  if  it  were  not  there  before,  we  admit  it  would  be 
false.     On  the  other  hand  it  can  not  be  given,  already  and  at 


Chap.  IV.]  THE  VALIDITY   OF   INFERENCE.  523 

the  Start,  for  in  that  case  we  should  have  no  inference  at  all. 
But,  if  so,  then  both  movement  and  issuing  change  are  false 
appearances  ;  they  belong  to  our  minds,  and  are  not  true  of 
things.  This  fatal  consequence  affects  all  inferences,  where 
the  middle  does  not  represent  the  cause.  And  then  the 
middle,  we  may  go  on  to  urge,  can  be  wholly  capricious.  It 
may  arise  from  nothing  but  our  arbitrary  act. 

For  consider  the  processes  of  distinction,  comparison,  and 
again  abstraction.  I  need  not  perform  these ;  I  experiment 
or  not,  as  it  happens  to  please  me.  But  is  it  possible  that 
whenever  I  happen  to  be  pleased,  the  things  have  somehow 
changed  themselves  harmoniously  }  How  frivolous  an  idea,  but 
how  inevitable  ;  and  yet  once  more  how  wholly  indefensible. 
We  have  hitherto  concluded  from  our  logical  postulate 
(which  assured  us  that  our  change  did  not  alter  fact)  that  the 
conclusion  was  there  and  came  out  to  be  seen.  But  now  we 
seem  confronted  with  three  alternatives.  Our  actual  process 
may  be  foreign  to  reality,  and  falls  outside  it  in  our  mental 
world.  Or  an  actual  afT^  answering  change  has  taken  place, 
and  the  facts  are  transformed  by  our  caprice.  Or  lastly  the 
course  of  things  runs  parallel  by  an  overruling  harmony.  Any 
one  of  these  alternatives  seems  attended  with  ruin. 

§  4.  (a)  Suppose  first  that  our  arbitrary  choice  has  modified 
the  facts  themselves,  that  no  quantities  are  equal  until  we 
have  compared  them,  nor  anything  different  before  we  have 
distinguished,  and  that  these  functions  make  the  object  which 
they  contemplate.  If  so  we  of  course  must  surrender  our 
postulate,  and  allow  the  result  to  become  conditional.  The 
things,  if  you  leave  them  alone,  are  not  equal,  since  equality 
depends  upon  your  caprice.  But,  with  this  result,  we  not 
only  give  up  what  before  seemed  true,  but  we  can  not 
accommodate  our  view  to  the  facts.  Unless  the  world  is 
quite  different  from  our  common  beliefs,  unless  we  turn 
upside  down  our  ideas  about  reality,  we  therefore  can  not 
accept  this  first  alternative.  And  if  (d)  we  next  make  trial 
of  the  harmony,  we  find  ourselves  still  immersed  in  difficulty. 
For  suppose  that,  when  I  argue,  the  world  is  changed,  and  a 
process  takes  place  conformable  to  my  movement,  then,  unless 
wc  think  that  the  world  goes  by  chance,  there  must  be  some 


524  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Ft.  II. 

kind  of  reason  for  that  change.  But  the  conclusion,  as  we 
have  it,  is  then  incorrect  ;  for  the  condition  of  the  process  is 
completely  ignored.  We  must  therefore  set  down,  not  A  by 
itself,  but  A  +  \;r  as  equal  to  C.  But  what  is  this  x  ?  If  it 
is  other  than  our  act,  then  once  more  the  things  diverge  from 
the  course  which  is  taken  by  our  thoughts. 

§  5.  "  But  the  X,''  I  shall  be  told,  "  though  it  is  not  the  act 
of  otcr  intelligence,  is  still  the  function  of  an  understanding. 
Phenomena  are  ruled  by  a  reason  not  mine,  and  my  argument, 
capricious  in  regard  to  its  existence,  is  compelled  and  subject 
in  respect  of  its  content.  If  I  make  it,  I  must  make  it  on  a 
certain  model,  and  this  model  is  the  work,  long  done  or  now 
doing,  of  an  inference  precisely  the  same  as  mine.  This 
double  process  of  a  two-fold  mind  unlocks  the  puzzles  by 
which  we  are  enclosed." 

I  should  be  sorry  to  seem  to  persist  in  unbelief,  but  I  am 
compelled  once  more  to  repeat  the  dilemma :  If  the  reality  in 
this  way  corresponds  to  logic,  then  reality  itself  has  been 
wholly  transformed.  One  may  perhaps  accustom  oneself  to 
regard  events  as  the  reasoning  sequence  of  the  divine  under- 
standing, but  it  is  not  so  easy  to  bring  under  this  head  any 
sameness  and  difference  that  is  thought  to  exist.  We  are 
forced  to  wonder,  if  things  by  themselves  are  really  not  alike, 
how  God  himself  can  find  them  the  same  ;  or  how  even  God 
goes  on  to  distinguish  them,  if  they  themselves  are  not  really 
different.  It  is  indeed  possible  here  that  a  distinction  might 
save  us,  that  a  sensuous  ground,  which  is  not  different,  when 
taken  together  with  a  function  of  the  intellect,  produces  alike 
both  distinction  and  difference.  And  yet  this  solution  is 
partial,  and  leaves  a  worse  puzzle  behind. 

We  might  perhaps  agree  that  reality  is  the  work  of  a 
reasoning  mind,  but  how  can  we  submit  to  the  belief  that  my 
reasoning  must  represent  reality  }  How  can  we  suppose  that 
each  trivial  argument,  every  wretched  illustration  that  we 
may  have  used  in  these  discussions,  provided  only  it  be  free 
from  flaw,  must  have  its  direct  counterpart  in  the  nature  of 
things.  You  may  suppose  that,  whenever  we  reason,  we 
retrace  the  solidified  logic  that  is  organic  in  the  world  ;  you 
may  believe  that  a  mind,  in  union  with  our  own,  brings  out 


Chap.  IV.]  THE  VALIDITY  OF  INFERENCE.  525 

by  one  process,  that  to  us  seems  double,  the  separate  sides  of 
existence  and  truth.  But,  on  either  view,  we  are  troubled 
with  this  consequence ;  every  possible  piece  of  mere  formal 
argument,  every  hypothetical  deduction  from  an  idle  fancy, 
all  disjunctive  and  negative  modes  of  demonstration,  must 
each  have  its  parallel  counterpart  in  reality.  This  con- 
sequence may  be  true,  and  I  will  not  deny  it.  But,  if  true, 
to  me  at  least  it  is  portentous.  Our  logic  will  have  secured 
correspondence  with  fact,  but  the  facts  themselves  have  been 
strangely  translated. 

§  6.  If  we  mean  to  keep  to  a  view  of  reality  which  is 
anything  like  our  common  ideas  (and  apart  from  a  system  of 
metaphysics  we  can  not,  I  think,  do  anything  else)  we  must 
come  in  the  end  to  our  third  alternative  (c).  We  must  admit 
that,  although  a  valid  inference  in  some  way  must  answer  to 
the  nature  of  things,  yet  at  least  some  reasoning  does  not 
show  that  nature.  It  exhibits  a  process  essentially  different 
from  the  actual  course  of  real  existence.  Even  if  you  believe 
that  it  comes  right  in  the  end,  yet  throughout  its  movement, 
it  diverges  from  the  truth.  Unless  you  revolutionize  your 
belief  about  reality  (and  perhaps  you  ought  to  revolutionize 
that  belief),  you  can  not  maintain  the  strict  correspondence  of 
thoughts  and  of  things. 

We  have  seen  so  far  that,  at  least  sometimes,  our 
movement  does  not  answer  to  the  course  of  reality.  But 
we  are  not  allowed  to  get  off  with  this  compromise.  We 
must  prepare  for  a  still  more  fatal  sentence.  We  shall  have 
to  see  that  our  mental  experiment  can  never  represent  the 
actual  event.  And  our  conclusions  also  are  threatened  with 
falsehood  ;  for  our  arguments  can  not  even  finish  with  a  truth. 
Both  process  and  result  diverge  from  given  reality.  They  no 
doubt  may  be  valid  in  the  sense  of  serving,  they  may  go  near 
enough  to  convey  the  meaning,  but  neither  can  be  called 
correct  translations. 

§  7.  If  the  result  seems  strange,  it  is  strange  because  we 
have  not  remembered  our  account  of  judgment.  It  is  in  a 
judgment  that  our  reasoning  must  end  ;  and  our  natural 
impulse  is  to  think  that  ideas  are  divided  and  joined  like  the 
things  which  we  know.     But  we  saw  that  this   notion  could 


526  THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  IL 

not  be  verified.  Our  hypothetical,  disjunctive,  and  negative 
judgments  were  none  of  them  found  to  represent  facts. 
There  was  nothing  left  which,  if  truth  is  a  copy,  could 
possibly  be  true,  save  only  the  class  of  categoric  judgments. 
And,  seeking  for  these,  we  failed  wholly  to  find  them,  so  long 
as  we  kept  to  the  series  of  phenomena.  All  our  ordinary 
truths,  every  single  affirmation  we  were  able  to  make  about 
the  course  of  events,  turned  out  in  the  end  to  be  hypothetical. 
We  tried  in  vain  to  get  right  down  to  the  facts ;  we  were 
always  left  with  an  artificial  extract  and  a  fragment  got  by 
mutilating  things.  And  this  product  failed  of  truth  in  two 
ways.  It  left  out  details  which  it  ought  to  have  copied,  and 
it  depended  on  details  which  did  not  exist.  However  you 
took  it,  it  turned  out  hypothetical,  and  the  elements  which  it 
connected  lacked  actual  existence. 

§  8.  And  this  failure  was  a  symptom  of  our  logical 
disease,  a  weakness  not  passing,  nor  local  in  its  area,  but 
deep-rooted  in  the  system.  For  judgment  and  inference,  if 
we  are  to  have  them  at  all,  must  both  be  discursive ;  they 
must  work  with  ideas.  But  ideas  do  not  exist,  and  they 
can  not  exist,  if  existence  means  presence  in  the  series  of 
phenomena.  I  do  not  mean  merely  to  press  the  obvious 
consequence  that  a  thing  can  not  be  in  two  places  at  once.  I 
do  not  mean  that  ideas,  being  inside  my  head,  can  not  also 
and  at  once  be  found  outside  it.  I  mean  much  more  than 
this.  Neither  outside  my  head,  nor  yet  inside  it,  can  ideas 
have  existence ;  for  the  idea  is  a  content,  which,  being 
universal,  is  no  phenomenon.  The  image  in  my  head  exists 
psychologically,  and  outside  it  the  fact  has  particular  ex- 
istence, for  they  both  are  events.  But  the  idea  does  not 
happen,  and  it  can  not  possess  a  place  in  the  series.  It  is  a 
mutilated  content  which,  as  such,  can  not  claim  to  be  more 
than  an  adjective.  And  the  functions,  that  work  with  these 
unrealities,  can  not  possibly  reproduce  the  flow  of  events. 

§  9.  This  discursive  nature  of  judgment  and  reasoning 
is  fatal  to  their  claim  of  copying  existence.  The  process  of 
the  inference  can  never  be  true,  and  the  result  can  never 
represent  the  fact.  We  will  not  waste  time  on  less  mortal 
objections  that  destroy  weaker  forms  of  logical  thought,  but 


Chap.  IV.]  THE   VALIDITY   OF   INFERENCE.  527 

will  at  once  proceed  to  the  strongest  instance.  Even  where 
the  middle  seems  to  answer  to  the  cause,  and  the  conclusion 
to  exhibit  the  actual  effect,  yet  even  here  the  movement  in 
the  mind  is  not  the  same  thing  as  the  movement  of  facts  ; 
the  premises  can  not  exhibit  the  conditions,  and  the  con- 
clusion is  very  different  from  the  consequence  in  time. 

In  our  inference  we  have  first  the  elements  apart,  then 
follows  their  union,  with  the  issuing  result.  But  the  elements 
that  occur  in  the  course  of  phenomena  do  none  of  them  possess 
an  isolated  being.  They  can  not  exist  every  one  by  itself 
Apart  from  one  another  they  indeed  may  be  found,  but  none 
separate  and  divorced  from  all  other  existence.  Yet  this 
context,  which  makes  them  real  as  events,  and  without  which 
they  could  not  appear  in  the  series,  is  ruthlessly  stripped  off 
in  our  mental  experiment.  And  so,  what  we  use  in  that  ideal 
synthesis,  is  nothing  but  an  artificial  preparation.  We 
operate  with  content  and  not  with  existence.  Our  elements 
are  nothing  in  the  world  but  adjectives,  and  adjectives  whose 
substantives  we  fail  to  state.  We  indeed  treat  them  as 
actual,  we  attribute  them  all  to  the  ultimate  reality  ;  but 
reality,  in  the  sense  in  which  we  have  chosen  at  present  to 
take  it  (the  sense  of  a  being  that  exists  within  the  series  of 
phenomena),  refuses  to  maintain  the  existence  of  our  elements. 
It  supports  them  hypothetically,  and  on  the  strength  of  con- 
ditions which  we  are  powerless  to  fulfil. 

§  10.  And  as  the  separation  of  the  elements  is  not  true, 
so  also  their  union  and  construction  is  fictitious.  I  will  not 
raise  again  a  former  objection,  though  it  weighs,  I  admit,  in 
the  adverse  scale.  If  our  minds  did  not  work  by  way  of 
construction,  the  premises  would  hardly  come  together  of 
themselves  ;  and  can  we  say  that,  in  the  outward  movement, 
there  is  anything  like  an  answering  activity?  We  will 
suppose  that  this  question  has  been  answered  in  a  way  which 
favours  the  claim  of  our  inference  to  truth.  But,  be  this  as 
it  rhay,  the  movement  in  our  mind  remains  discursive 
symbolic  and  abstract.  If  the  facts  come  together  on  just 
the  same  principle  on  which  we  unite  our  ideal  elements,  yet 
they  can  not  come  together  in  just  the  same  way.  The  real 
is  divided  from  the  mental  union  by  an  insuperable  difference. 


528  THE   PRINCIPLES   OF   LOGIC.        [Bk.  III.  Pt.  IL 

The  synthesis  of  facts  may  be  partly  the  same  as  our  mental 
construction  ;  but  in  the  end  it  diverges,  for  it  always  has 
much  that  we  are  not  able  to  represent.  We  can  not  exhibit 
in  any  experiment  that  enormous  detail  of  sensuous  context, 
that  cloud  of  particulars  which  enfolds  the  meeting  of  actual 
events.  We  may  say  indeed  that  we  have  the  essential  ;  but 
that  plea  reiterates  the  charge  brought  against  us.  It  is  just 
because  we  have  merely  the  essence,  that  we  have  not  got  a 
copy  of  the  facts.  The  essence  does  not  live  in  the  series  of 
events ;  it  is  not  one  thing  that  exists  among  others.  If 
reality  is  the  chain  of  facts  that  happen,  then  the  essence  is 
a  creature  which  lives  only  in  the  thought  which  has  begotten 
it.  It  could  not  be  real,  and  it  can  not  be  true.  Our 
construction  is  as  false  as  our  separate  premises. 

And  our  conclusion  can  hardly  fare  much  better.  Be- 
gotten of  falsehood  it  can  not  so  far  be  misbegotten,  as  to 
show  us  in  the  end  the  features  of  fact.  The  parental  disease 
still  vitiates  its  substance.  Abstract  and  symbolic  it  mutilates 
phenomena  ;  it  can  never  give  us  that  tissue  of  relations,  it  can 
not  portrays  those  entangled  fibres,  which  give  life  to  the 
presentations  of  sense.  It  offers  instead  an  unshaded  outline 
without  a  background,  a  remote  and  colourless  extract  of 
ideas,  a  preparation  which  everywhere  rests  on  dissection  and 
recalls  the  knife,  a  result  which  can  not,  if  events  are  reality, 
be  aught  but  unreal. 

§  II.  And  no  possible  logic  is  exempted  from  this 
sentence.  If  we  recur  to  that  type,  which  we  found  or 
fancied,  where  the  real  and  the  logical  seemed  wholly  one, 
if  we  come  in  the  end  to  the  Dialectic  process,  we  can  not 
escape  the  point  of  the  objection.  For,  if  the  starting-place 
we  leave  were  real  by  itself,  if  it  were  actual  so  as  it  first 
comes  before  us,  what  sufficient  excuse  can  we  plead  for 
leaving  it?  Why  do  we  correct  and  supplement  it,  if  it  is 
true  }  You  may  say  that  a  parallel  alteration  and  amendment 
is  the  actual  course  of  the  genuine  reality,  but  I  confess  to 
my  mind  that  solution  is  a  failure.  If  you  think  that  the 
element,  with  which  you  began,  was  apart  by  itself  in  the  field 
of  reality  and  within  that  vacuum  began  tQ  develope,  then  to 
me  the  whole  question  is  lost  in  darkness.     But  if  you  admit 


Chap.  IV.]  THE   VALIDITY  OF   INFERENCE.  529 

that  a  movement  took  place  by  virtue  of  the  action  of  the  total 
system )  then  surely  we  must  add  that,  apart  and  by  itself,  our 
element  was  not  real.  Both  its  isolation  and  its  subsequent 
evolution  took  place  within  a  completed  universe,  and  without 
that  universe  would  have  been  nonentities.  And,  if  so,  our 
process  is  but  partially  true.  It  depends  on  conditions  which 
it  fails  to  state.     It  does  not  answer  to  the  working  reality. 

Both  our  starting-place  and  our  process  of  advance  and  the 
provisional  goal  at  which  we  arrive,  are  none  of  them  true  of 
the  actual  world.  If  you  take  them  by  themselves,  they  can 
hardly  be  more  than  our  way  of  thinking.  Our  knowledge 
and  reality  would  never  be  one,  until  in  our  minds  the  self- 
conscious  Universe  were  to  follow  itself  throughout  all  its 
productions,  and  comprehend  itself  in  the  whole  of  its  detail. 
And,  if  that  pass  were  reached  and  that  hope  consummated,  it 
is  doubtful  if  then  our  knowledge  would  be  logical,  and  if  it 
could  still  bear  the  form  of  a  discursive  process. 

§  12.  It  seems  hardly  worth  while  to  follow  any  further 
this  line  of  objection.  We  may  however  recall  a  further 
point,  with  which  we  will  bring  the  discussion  to  a  close. 
Even  if  the  process  of  our  logical  movement  seemed  ideally 
to  counterfeit  the  course  of  phenomena,  and  to  present  us  with 
the  actual  changes  of  events,  yet,  if  this  by  any  means  could  be 
believed,  we  still  fall  at  the  end  into  hopeless  confusion.  For 
if  it  were  not  for  our  inferring,  we  never  should  have  had  this 
series  of  phenomena.  It  is  not  merely  the  separate  strands 
and  fibres  of  causation,  but  it  is  the  whole  continuity  of  the 
total  series  which  is  absolutely  based  on  ideal  reconstruction. 
By  means  of  this  function,  and  this  function  alone,  we  have 
connected  the  past  in  one  line  with  the  present.  It  is  by  this 
alone  that  we  have  acquired  our  knowledge  of  phenomenal 
changes  ;  and  it  is  this  creation  we  approach  with  that  series  of 
inferences  which  attempts  to  exhibit  the  threads  of  causation. 
But  if  reality  is  not  to  be  the  work  of  our  reasoning,  if  it  is  to 
lie  within  mere  presentation,  then  the  train  of  events  are  them- 
selves not  real.  They  themselves  are  nothing  but  a  false  con- 
struction ;  and  a  mental  sequence  that  portrayed  them  truly, 
as  we  believe  them  to  exist,  would  itself  be  therefore  untrue  to 
given  reality. 

2  M 


530  THE   PRINCIPLES  OF   LOGIC.        [Bk.  IIL  Pt.  II. 

For  unless  we  think  that  phenomena  can  be  real,  though 
they  appear  to  no  one,  we  must  hold  that  the  past,  at  least 
as  we  know  it,  has  no  existence  outside  reproduction.  But  we 
know  what  is  past  by  synthetical  judgments,  and  they  are  a 
function  which  depends  on  a  ground.  This  ground  is  the 
principle  of  the  Identity  of  Indiscernibles ;  it  is  because  the 
ideal  content  seems  the  same,  that  we  therefore  assume  it  to  be 
really  identical,  and  identical  in  spite  of  change  and  diversity? 
despite  the  difference  of  its  two  presentations.  But  how  shall 
we  dare,  on  the  strength  of  this  principle,  to  treat  the  ideal  as 
if  it  were  real }  What  help  could  we  expect  from  the  School 
of  Experience,  if  our  only  way  to  rehabilitate  their  fact  is 
to  violate  their  most  sacred  and  continuous  tradition?  Can 
we  safely  go  from  the  appearance  of  sameness,  within  the 
mind  which  compares,  to  a  real  identity  that  connects  events  ? 
Can  we  pass  from  ideal  redintegration  to  actual  continuity  of 
fact  ?  If  we  can  not,  then  forthwith  the  series  of  phenomena 
becomes  unreal,  and  our  reasoning  which  follows  the  chain  is 
illusory.  But,  if  we  can,  then  at  once  our  idea  of  reality  is  quite 
transformed.  Our  reasoning  will  be  true  because  the  facts  are 
themselves  inferential.  We  thus  either  have  relinquished  the 
presumption  that  reality  lies  in  what  is  given  to  sense,  or  are 
compelled  to  admit  that  a  serial  reality  is  itself  a  bad  in- 
ference.    On  either  alternative  we  have  ended  in  confusion. 

§  1 3.  To  sum  up  the  result — if  reality  consists  in  an  actual 
sequence  of  sensuous  phenomena,  then  our  reasonings  are  all 
false  because  none  of  them  are  sensuous.  And  still  more  if 
reality  is  wholly  confined  to  the  given  in  presentation,  then  the 
inferences  which  try  most  thoroughly  to  follow  the  facts,  are 
therefore  and  on  that  account  the  most  false.  And  reality,  it 
would  seem,  must  be  thus  confined,  since  its  prolongation  is 
merely  ideal.  It  is  lengthened  on  the  strength  of  the  Identity 
of  Indiscernible  Content,  and  it  ends  in  a  link  which  is  ideal  also. 
The  past  can  not  be  restored  in  its  sensuous  fulness  ;  the  detail  is 
not  literally  present  to  the  mind.  It  is  judged  to  be  there  ;  but 
such  judgment  is  nothing  but  a  general  indication,  a  symbolic 
reference  to  a  context,  whose  main  character  and  import  still 
survives,  but  whose  complex  particulars  are  perished  irreco- 
verably.    And  in  the  end  we  are  forced  to  hold  to  one  of  these 


Chap.  IV.]  THE  VALIDITY  OF  INFERENCE.  531 

conclusions  ;  our  reality  is  not  that  which  appears  to  our 
senses,  or  else,  if  truth  is  to  present  us  with  facts^  our 
reasonings  are  every  one  of  them  false. 

§  14.  It  is  idle  to  urge  the  argument  from  success.  It  is 
useless  to  reply  that  the  mass  of  our  results  is  enough  to  prove 
the  truth  of  our  presumption,  and  to  show  that  our  reasonings 
are  identical  with  fact.  You  can  not  plead  that,  because  logic 
works,  logic  can  not  be  wrong.  For  the  answer  is  simple.  If 
logic  succeeds,  then  logic  is  not  wrong  to  work  as  it  does  work. 
It  is  practically  right  beyond  all  suspicion,  but  for  all  that  it 
may  rest  on  theoretical  error.  It  must  answer  to  facts  so  far 
indeed  as  to  answer  our  purpose,  but  withal  its  assumptions 
may  be  downright  false,  and  its  principle  may  turn  on 
unblushing  fictions.  You  can  not  assert  that,  if  a  science  goes 
right,  that  science  is  unable  to  start  from  false  premises. 
Have  not  brilliant  results  in  the  study  of  nature  been 
obtained  by  the  help  of  such  working  hypotheses  as 
hardly  pretended  to  be  more  than  fictions }  And  why 
should  not  logic,  if  it  shares  the  success,  share  also  in  the 
falsehood?  We  should  surely  be  satisfied  if  discursive 
necessity,  though  itself  nothing  real  and  not  strictly  true, 
runs  parallel  with  reality,  and  is  throughout  corresponding  to 
our  practical  needs. 

§  15.  For  this  seems  the  dilemma  to  which  we  are  brought. 
If  we  keep  to  the  ordinary  belief  as  to  fact,  or  to  anything  that  is 
like  that  ordinary  view,  then  either  our  account  of  the  nature 
both  of  judgment  and  reasoning  must  be  radically  wrong,  or 
else  these  processes  are  no  proper  counterpart  of  the  accepted 
reality.  We  can  not  at  the  end  of  these  toilsome  marches 
accept  the  failure  of  our  whole  expedition ;  and  we  are 
led  to  seek  for  a  place  of  provisional  rest  in  the  second 
alternative.  And  perhaps  it  is  not  our  reasoning  that  will 
suffer  a  loss  of  dignity.  Why  should  not  that  view,  which 
finds  reality  within  the  series  of  temporal  events,  be  itself 
degraded  to  the  rank  of  an  illusion  }  Why  should  not  the 
result  of  the  deepest  philosophies  after  all  be  the  truth,  and 
our  sensuous  presentment  be  misrepresentation  that  can  not 
give  fact  ?  In  this  case,  if  our  logic  diverged  from  the  given, 
it  perhaps  after  all  has  been  wiser  than  it  knew  of     Unawares 


532  THE   PRINCIPLES   OF   LOGIC.        [Bk.  in.  Pt.  IL 

it   has   followed   the   hidden   reality,    and   against  itself  has 
throughout  been  true. 

Possibly  this  may  be,  and,  if  so,  an  old  dream  would 
gain  fulfilment.  But  too  probably,  again  at  this  final 
moment,  a  rival  alternative  might  shatter  our  hopes.  Al- 
though the  reality  is,  for  certain  and  assuredly,  no  series  of 
phenomena,  may  it  not  still  be  something  other  than  thought, 
or  contain  at  the  least  an  alien  element?  Then,  if  so,  this 
genuine  fact,  when  we  found  it,  would  remain  out  of  one- 
ness with  discursive  intelligence,  or  intelligence  altogether. 
Our  logic  after  all  may  turn  out  to  be  false,  if  triith  means 
complete  identity  with  the  real,  or  implies  an  accurate  un- 
falsified  copy. 

§  1 6.  But  what  is  it  guarantees  this  presumed  identity 
of  truth  and  fact  ?  We  have  an  instinct,  no  doubt,  that  leads 
us  to  believe  in  it,  but  our  instincts,  if  they  can  not  be  in 
error,  may  at  least  be  mistranslated  and  misunderstood.  And 
here  we  seem  placed  between  rival  promptings,  that  contend 
for  mastery  over  our  reason.  It  is  an  old  preconception  that 
reality  and  truth  must  contain  the  same  movement  of  a  single 
content  that,  by  itself  not  intellectual,  then  doubles  itself  in 
the  glass  of  reflection.  On  the  other  hand  it  is  a  certain  result 
that  our  intellect  and  the  movement  of  our  intellect's  content 
is  abstract  and  discursive,  a  mere  essence  distilled  from  our 
senses'  abundance.  And  this  certainty  has  inspired  an  opposite 
conclusion.  Since  the  rational  and  the  real  in  truth  must  be 
one,  and  since  these  vital  essences  are  the  life  of  our  reason, 
then,  despite  of  seeming,  the  reality  too  must  consist  and  must 
live  in  them.  If  the  real  becomes  truth,  then  so  without 
doubt  the  truth  must  be  real. 

In  the  face  of  these  promptings,  I  must  venture  to  doubt 
whether  both  have  not  branched  from  one  stem  of  deceit, 
whether  truth,  if  that  stands  for  the  work  of  the  intellect,  is 
ever  precisely  identical  with  fact,  or  claims  in  the  end  to 
possess  such  identity.  To  the  arguments  urged  by  the 
reason,  and  which  demonstrate  that  an  element  which  is  not 
intelligible  is  nothing,  I  possibly  might  not  find  an  intelligible 
reply.  But  I  comfort  my  mind  with  the  thought  that  if 
myself,  when  most  truly  myself,  were  pure  intelligence,  I  at 


Chap.  IV.]  THE  VALIDITY  OF  INFERENCE.  533 

least  am  not  likely  to  survive  the  discovery,  or  be  myself 
when  I  wake  from  a  pleasant  delusion.  And  perhaps  it  may 
stand  with  the  philosopher's  reason,  as  it  stood  with  the 
sculptor  who  moulded  the  lion.  When  in  the  reason's 
philosophy  the  rational  appears  dominant  and  sole  possessor 
of  the  world,  we  can  only  wonder  what  place  would  be  left  to 
it,  if  the  element  excluded  might  break  through  the  charm  of 
the  magic  circle,  and,  without  growing  rational,  could  find  ex- 
pression. Such  an  idea  may  be  senseless,  and  such  a  thought 
may  contradict  itself,  but  it  serves  to  give  voice  to  an  obstinate 
instinct.  Unless  thought  stands  for  something  that  falls 
beyond  mere  intelligence,  if  "  thinking  "  is  not  used  with  some 
strange  implication  that  never  was  part  of  the  meaning  of  the 
word,  a  lingering  scruple  still  forbids  us  to  believe  that  reality 
can  ever  be  purely  rational.  It  may  come  from  a  failure  in 
my  metaphysics,  or  from  a  weakness  of  the  flesh  which 
continues  to  blind  me,  but  the  notion  that  existence  could  be 
the  same  as  understanding  strikes  as  cold  and  ghost-like  as 
the  dreariest  materialism.  That  the  glory  of  this  world  in  the 
end  is  appearance  leaves  the  world  more  glorious,  if  we  feel  it 
is  a  show  of  some  fuller  splendour ;  but  the  sensuous  curtain 
is  a  deception  and  a  cheat,  if  it  hides  some  colourless  move- 
ment of  atoms,  some  spectral  woof  of  impalpable  abstractions, 
or  unearthly  ballet  of  bloodless  categories.  Though  dragged 
to  such  conclusions,  we  can  not  embrace  them.  Our  principles 
may  be  true,  but  they  are  not  reality.  They  no  more  make 
that  Whole  which  commands  our  devotion,  than  some  shredded 
dissection  of  human  tatters  is  that  warm  and  breathing  beauty 
of  flesh  which  our  hearts  found  delightful. 

§  17.  But  be  this  as  it  may,  one  result  is  most  certain.  If 
these  pages  have  not  erred  from  beginning  to  end,  there  is  at 
least  one  thing  which  we  are  safe  in  rejecting.  No  cheap  and 
easy  Monism  can  stand  before  an  enquiry  into  logic.  The 
parallel  series  of  sense  and  of  thought,  phenomena  presented  by 
simple  observation  and  reasoning  that  retraces  the  chain  of 
presentations,  may  both  be  banished  to  the  region  of  illusions. 
If  the  string  of  appearances  could  possibly  appear,  if  con- 
ceivably their  sequence  could  be  given  as  fact,  yet  assuredly 
logic   could   never   reproduce   them,    nor   supply   us   with   a 

2    N 


534 


THE   PRINCIPLES   OF   LOGIC.        [Bk.  IIL  Pt.  II. 


truthful  counterpart  and  copy.  The  desire  to  comprehend 
our  Universe  as  the  double  outgrowth  and  revelation  of  a 
single  principle,  depends  on  a  genuine  impulse  of  philosophy. 
It  will  hardly  be  fulfilled  without  patience  and  criticism,  and 
never  if  we  start  with  a  blind  acquiescence  in  the  coarsest 
prejudices  of  popular  thought. 


THE   END. 


LONDON :    PRINTED    BY   WII.MAM    CLOWES    AND   SONS,   I-IMITEDi 
STAMFORD   STREET   AND    CHARINvi   CROSS, 


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